They are seperate 1x12 speaker cabinets, not powered and can each handle at least 200 watts. Basically all I need is an appropriate power amp right? My sound card --> poweramp--->
speakers. I play along with background tracks on Guitar Pro but need more oomph!
Here's a pic of them:

Yes, you should be able to run them. However, if they're not magnetically shielded you can't put them near your computer. Computers and magnets don't mix too well.

Personally, I'd just get louder speakers, my 500 watt computer speaker system keeps up nicely with my amp.
Its possible. You would run from your computer's line out into some kind of amplifier (home stereo probably) via a 3.5mm jack (make sure its stereo) to RCA jacks more than likely.