Confusingly Poor System Performance

Not sure if this is the correct subforum, so moderators feel free to move this thread to a more appropriate location.

Specifications
CPU: Intel Core 2 Duo E8400 3.00 GHz
PSU: 420W
Graphics card: NVIDIA GeForce 9800 GT
Mobo: Gigabyte EP45-UD3R
RAM: 4GB Corsair RAM
Hard drive: 1TB Western Digital
OS: Windows 7 Ultimate

So in the past few days my computer has been shutting down when put under what was once normal stress (e.g. playing a game, watching a League of Legends stream, etc.) Even when browsing the internet or watching YouTube the computer will occasionally shut down with no warning. Before this problem began, the screen would occasionally go dark, and I'd have to restart the computer. I could still interact with the programs on my computer (I know because I could continue a Skype call even after the monitor blacked out), but couldn't see anything and couldn't recover the display. I did a virus scan with Avast and discovered a few infected and corrupted files that I took care of (including a Trojan). I then did a clean install of Windows 7, re-installed Avast, and ran another quick scan. No problems there. Did all the recommended Windows software updates as well. Even after all this, clean install included, the computer crashed after a few minutes of internet browsing and watching a League of Legends stream. After this, I ran the Resource and Performance monitor, which gave me poor results: CPU, Gaming graphics, Graphics, and Disk ratings were all poor and Memory was very poor. Ran a defrag analysis on my hard drive and found that 2% is fragmented and am going to defrag now, though I don't think that'll solve my problem.  

What can I do to pinpoint the source of all this poor performance? Is it merely the age of my hardware? Is it caused by a specific part?

Any help is greatly appreciated. Thanks.