If you have Chillisoft on your linux box then you should be able to run most of the ASP code.
The challenge that you face is connecting the code to the database. SQL Server 2000 will not run on a Linux box and any workarounds really aren't advisable.
You could port the database to MySQL and if the ASP code has been written well, it should be easy to make a few changes to connection strings etc to get the ASP code talking to the MySQL database.
An alternative is that your hosing company may offer shard SQL server hosting on their own Windows boxes. OR you could host the SQL server database elsewhere and connect directly to it using an IP address.
Where you may have difficulties with the ASP code is where 3rd party components have been used for uploading, image manipulation and massmailing etc. These probably won't run on a Linux box.
For a full run down on what does and doesn't work on ChilliSoft check out this page http://info99.sch.bme.hu/asp_dif.html
There are also programmes to automagically convert ASP to PHP which could do the bulk of the work for you and then have a PHP programmer check it all over to make the final tweaks.