First, your term "access" can have many meanings:
access = "keep a link or connection with"
access = "get or read some data/info/code from of your computer"
access = "put or install some data/info/code/virus onto your computer"
If you meant the first... the answer is a yes. This means the ISP's "computer" (or network switch) can (and does) regularly (every few seconds/minute) send a "ping" type of message to your computer (actually to your network card/router hardware) to see if it's connected. The ISP will keep its own ports ("connecting wires") connected/busy only if it has to (if you've connected and are using their internet-link). It doesn't want to keep checking "unused" ports if there's no computer waiting on the other end. So it does this by sending a very simple "Are you there?" request to every computer... including yours. Your computer's hardware (not the software or operating system) automatically responds to say that it IS connected to them. So in this sense, the ISP's computer can and does (and is supposed to) "access" your computer. However, this access does not let them read any info from your computer (or its hard disk), and does not let them write/install anything onto your computer. This is only an "electrical" signal exchanged... that tells them your computer is still there. Basically, this type of "access" tells the ISP that your computer is "on" and wants to "talk" over the internet. But no data gets exchanged as part of this. This doesn't even use or need your browser -- it's fully at the hardware level. Your computer's CPU might not even get involved, to do this (this depends on your network card/router/hardware -- more expensive/sophisticated computers will do it fully in hardware).
As to the other two: (either malicious reading from/writing to your computer)... the simplest basic answer -- (if you're not including the possibility of hacking or infiltration or an sophisticated exploit) -- is a definite No. Data can be read from/written to your computer only if your computer lets another system do it. Actually, no other computer can ever read or write anything on your computer... the "reading" or "writing" can ONLY be done by your computer. If some other computer is trying to read, your computer must give your data that the other computer asks for. So if your computer doesn't give something off of its hard-disk... no computer can "take" anything. Same applies to writing data onto your computer -- this also requires your computer's full participation (since ONLY the hardware in your computer/CPU is physically connected to your hard-disk -- so only your computer's CPU can write something to your hard-disk).
And operating systems (like Windows 10 or Linux or Mac or Android or iOS or whatever) do not send data/info out to any system that "asks". It sends data/info only based on built-in security settings/features. And all modern computers and devices have a basic level of security built-in, where they don't give its own data just to anyone. Just as you won't give your property/items to anyone who comes to your home's door or window.... neither will a computer. The Operating System won't, and the software (like a browser) won't. They are not programmed/designed to "hand over" stuff, or to "accept" stuff from stranger computers.
Alternatively...
if you're asking about unusual or "extreme" exploits/infiltration... theoretically it is possible, but highly unlikely. And this is possible ONLY from any bug or virus(bad software) or missing/unset security-feature ALREADY EXISTING in your computer. For example, Windows has bugs (that Microsoft regularly sends "patches" to fix). So do other software, like browsers. This is why you/we all have to install every patches (especially those related to vulnerabilities or security). If you keep doing this, then your computer and its software will be mostly safe.
However, there's always the possibility that there's an unknown and un-patched bug existing... (or a very rare "situation" or "event" that Microsoft added to the OS, either intentionally or due to misunderstanding, or a programmer's error). This would leave a hidden vulnerability in Windows. Many "exploits" actual exploit (use) such hidden bugs/vulnerabilities in the operating system or browser. However, it's very difficult to use these "latent" bugs. If it was easy to find, Microsoft or others would have found them already (and fixed them already). So in the real world... every software (including Windows) does have intrinsic but very hard-to-find and hard-to-use bugs/vulnerabilities. Eventually, after a few years, a small group or a person will find one of these latent bugs. They might publish a story about it somewhere on the web... and after a few months another person might figure out a way to use that exploit... to do something nasty. Then word gets around the internet that this new exploit is being used... and smarter people (white hat hackers) get involved to figure out how they're doing it... and they find a solution that they then tell the software maker (Microsoft). Then Microsoft sends/issues a patch/fix that fixes the bug. This is why you should install patches that you are requested to.
There is another type of vulnerability that does not depend on Microsoft or the software on your computer. That has to do with how you installed or configured your computer/operating system/network/WiFi/Router. These things are all under your control (or whoever setup your system/network). For example, when you first install a modern OS, you have to create an administrator's account with its own password. If you set this password to something very simple (like "123" or "password")... this makes your system very easy to hack into. You'd be surprised how many people use passwords like "password" or "password1" or "password7". Many exploits automatically use a few hundred of these "easy" passwords. So if you setup your computer but you left many security features not properly setup... for example whether any user is able to install software or not... these weaknesses (that you've left/setup) can be taken advantage of.
So... given that every computer has bugs/vulnerabilities (from the software maker) and settings mistakes (from you or whomever setup your system)... these are the ONLY ways someone else can gain access to your system. However, even if your system has vulnerabilities, it is still very difficult. And in the normal case... harder if you have unique systems or modifications to your system that the "average" computer doesn't have. For example, if your computer has hardware-encryption of all reads & writes to your hard-disk... this provides a major wall (protection) to your computer... and only very special bugs/hacks can get past it. But few computers have such strong data protection. Similarly, you can install some protections on your network path/connection (the simplest is a good "firewall"). Another factor is your behavior on the internet. If you go to "any" site, and don't have a virus-protection installed, and allow popups, etc... these again are settings and safety-software on your computer... these leave you more vulnerable. Rather, if you browse the web using safe methods (you check a link/URL before clicking on it)... you don't go to unknown or strange sites... or sites that your browser warns you about.... you will generally be safe. These behaviors/steps will stop probably 99%-99.999% of attacks.
All of this assumes a malicious entity/person/group outside your network is trying to hack/enter your system, to exploit latent bugs/vulnerabilities/settings. No normal ISP would do that (unless you're using an unknown or disreputable ISP -- if so... change). Major/reputed ISPs would never intentionally do something to break/infiltrate your system.
It's possible that the ISP's one computer (somewhere on their network) has a virus... and that virus finds its way out to yours -- but that virus would need help (from a bug/vulnerability on your system -- it can't "attack" your system without your computer's help). And again if your ISP is a major/reputable firm, they would be regularly (daily?) checking their systems to ensure they have no virus. This also reduces the chances. If your ISP's network/computer is bug-free and virus-free, and so is your computer... then it's nearly 0% chance of their system attacking/infiltrating yours.
The last possibility is that the ISP could be ordered (through a legal court order) to intentionally infiltrate your computer. This is of course very rare... and would require law-enforcement or higher government authority's role. If the government is after you or your computer's data... then there isn't much you can do to stop them (in that case, asking here won't get you answers).
Hope this answered what you were wondering.
:)