Are both computers logged in to the same iTunes account? If so, you can redownload the apps for free, either directly from the iPod or onto the computer you sync with.
Or on a PC, app files are stored in your iTunes\Mobile Applications directory. You can copy the app files off from one computer and into the other one, drag them into iTunes, then sync. I believe with a Touch, you can sync apps from one machine and media (music, videos) from another. However, *all* apps need to be synced from one computer -- you can't have some apps on one and some on another.
Oh, and here's another idea. Provided both computers are on the same iTunes account, try right-clicking on the Touch icon in iTunes, and select "Transfer Purchases." This should copy all the apps currently on the Touch onto the computer. The computer now has apps on the touch + apps that were downloaded to it, and you can now sync the whole set onto the touch. Again, I don't think this will erase any media off the Touch, but I can't 100% guarantee that part.