Ok, now I have something to work with...
that GTX9800 and X2 processor are (relatively speaking) quite old now - I wouldn't go for the CPU as a possible culprit though - those rarely fail "a bit"
The graphics card though is a possibility, as is the PSU (assuming all components are of a similar age) - some of the components on/in there (specifically capacitors) could be on their way out.
YouTube and Flash stress systems in an entirely different way than gaming does, Video playback stresses parts of the graphics subsystem that aren't used at all by gaming (hardware MPEG decoding) and I've seen Flash games bring down an otherwise completely stable system for no apparent reason (later traced to a faulty PSU).
Capacitor failure can be easy to spot (the tops are supposed to be flat and one sign of failure is them poking up into a dome shape or oozing brown crap) - have a look around the graphics card and shine a torch through the vents in the PSU...
I'd be inclined to disregard the motherboard as a source of the problems too as I generally find gigabyte boards to be pretty reliable (I'm typing this on an AM3+ one right now)
Of course, all my hardware diagnosis ideas count for naught if your problem is down to some software issue (you did run a full virus and malware scan I assume? - I'd recommend Avast for anti-virus and spybot search and destroy for the malware side).