I've never really come across an all-in-one software diagnostic package that could diagnose any and all hardware errors. Closest I've seen has been the PC-Doctor bootable diag that HP leases for their warranty work, and even that's not exactly comprehensive.
There are a few individual tests you can run that will help you narrow things down, though. Hard drive and RAM have reliable tests you can run to verify they're working properly. HD Tune and the IBM/Hitachi Drive Fitness Test are good universal hard drive diagnostics. I prefer Memtest+ to check RAM integrity. Both the DFT and Memtest+ are available on the Ultimate Boot CD
, I highly recommend burning a copy of that and tucking it away in your CD collection.
If you think it's a problem with your video card, try loading programs that will stress the card and see what happens. (What makes you think it's the card, BTW?) 3D game demos are handy for this.