Harddisk or software or virus/

I have an iMac, 4 years old. OS X 10.6.4 Snow Leopard. I get stuck in various stages of working with it: sometimes after 15 minutes, sometimes even when starting up. The coloured spinning wheel appears and nothing happens, nothing works anymore. I ran Disc-repair and it said I had nothing wrong with my harddisk. I tried to re-install Snow Leopard, but it would n't work. Now I formatted the harddisk and tried to re-install Snow Leopard, but that wouldn't work either. So I installed Tiger and that worked as it should. When I tried to install Snow Leopard then, it wouldn't work again, so now I am installing Leopard and I hope I'll be able to install Snow Leopard after that. Fortunately I have a copy of all my work in Time Machine.
Has anybody had this problem before? Is it a problem in the software, the harddisk o a virus. ClamXav came up clean. The problem remained with all Airport turned off and the firewall on.

My first guess would be a hardware issue. Start with the Apple Hardware Test:

Intel-based Macs: Using Apple Hardware Test

Its certainly not a virus

How much RAM does that machine have - 2 gig should be fine for Snow Leopard

I would run the latest combo update after installing Snow Leopard
Mac OS X 10.5.6 Combo Update

Then download ONYX and run a permission reapair and keep ONYX for any future maintenance tasks
Apple - Downloads - System/Disk Utilities - OnyX

... and what cwa107 says ^^^

Sounds like the hard drive is on the way out. it is not a virus ~ no viruses for Mac OS X.