You don't say what kind of computer you have, but since you say your machine got a virus and Macs don't have any viruses, I have to assume you mean a PC.
If I'm interpreting your light-on-details post correctly, you do have some or all of your 800 song library on your iPod Touch. Can you put those back into iTunes on your computer now that the computer's issues are resolved? Yes.
You'll need some third-party software to do this. BEWARE any that purport to be "free." They're not and/or they are not effective.
The one I would recommend is called
Pod to PC for Windows computers. It not only recovers the songs, but the ratings, playlists, stat info, cover art, and photos (if any) and more. It costs $20, money well spent IMO.
Starting this fall, Apple will be offering a free service called iCloud that will automatically back up iTunes purchases to avoid this problem. You might want to see if you can sign up for that when it becomes available.
As for re-downloading, Apple generally does not allow re-downloading of music (they occasionally make exceptions, but you shouldn't count on that and should use recovery software like the one I mentioned). This is not Apple's fault, it's a restriction of the music copyright holders (ditto for movies and TV shows).
Apps, however, are not restricted in this way: if you lose a copy of an app you bought, you can re-download it 1,000 times if you want to, free of charge. So between Pod to PC and re-downloading apps, you should be able to recover pretty much everything that was on the iPod Touch with no real issues.