Generally those symptoms aren't related to software: it could be a failing power supply or (more often) a bad RAM module, even a mobo failure (I had this problem on a mobo with condensers leaking brownish stuff). If you're able to boot in safe mode, do some stress tests. Start with a torture test with Prime95, doing at least some cycles. This will test only your CPU and your RAM. If it fails doing it job and halts you could have some bad RAM. You can also try Memtest86, but sometimes it fails to discover some issues: but at least, if it shows some errors, you most likely have some faulty RAM, so you can test some other modules and see if they're fine. Prime95 is a bit more picky, but it cannot identify the problem, it just shows you have one (CPU? Mobo? RAM?). Then use some more general benchmarks that test your hardware. Use HDTune to test both health and performance of your hard disk. Check voltage stability of your power supply, if you can compare voltages with suggested values.
Generally, however, it is a good idea to test hardware without running the OS on your hard disk: prepare (or have someone prepare it for you) an UBCD for Windows, most diagnostic tests are already there: it's useful and not time consuming. The GPU is the only component that may need a test with your original OS.
On the software side, you could have some nasty rootkitted software. I can't tell you how to look for rootkits since it's a job that requires some OS knowledge, but anyway if you look for some anti-rootkits you'll find them on the net. You MUST know how to use them anyway, so I won't enter the discussion. My favourite one, however, is GMER. And, absolutely, ditch Task Manager in favour of Process Explorer, and get a serious antivirus. Symantec is evil. If you have some suspects about a single file, virusscan.jotti.org is what you need, but it's sometimes very busy, so you have to wait in line. Otherwise go for housecall.trendmicro.com or other online scans (like Panda) for a faster job.