Did you really mean both attachments AND links? Those are two different processes. You emphasize that links don't work so I'll focus there. Links are invoking your browser and all PCs have a browser. WIndows won't work with Internet Explorer. Some thoughts:
1. did you recently switch browsers? For example, if you use Firefox, consider reinstalling it and resetting as the default browser.
2. did you recently switch or upgrade your email program? This is an area to check carefully, since your email program isn't invoking your browser and also is not invoking applications (e.g., Word) that it was doing earlier. Since application programs and browser links live in two different worlds, the email program is suspect.
If you're not aware of any changes, my suggestion would be to reinstall your email program. Another analytical approach would be to install an additional email program. For example, if you use Outlook Express for email, then install Thunderbird. If Thunderbird works fine, then you will know that Outlook Express is somehow corrupted.
I know your problem sounds complex, but generally this is not a complicated fix. Good luck... :)