This assumes you are running XP on your 'spare' computer (Don't know if this works with Vista). Go to Amazon and order one of
these. While your waiting :
, head off to 'tinternet and download
this - its free!
Install it on your 'spare' computer. Once you get the caddy from Amazon, remove the HDD from the PC with the deleted files, connect it to the caddy (with the PSU if needs be), then connect it to your 'spare' PC. Let it detect - it should find a new HDD and ask you what you want to do with the files - do nothing. Then run the Recovery software and let it scan all your drives - it may take some time. When its finished it'll list what its found - hopefully your files will be there. If so, copy them to your spare PC, disconnect the caddy, put the HDD back in the other computer.
Copy the files across via cd-rom, memory stick, etc and bob's a man your mothers sister married.
If you need further advice, PM me.