The hardware or the software?

I've recently built my first computer system and when it works, it works great. It's supposed to be for light gaming until I can afford a decent graphics card.

I've run into a few problems however.
- random BSODs while performing some task
- game will randomly crash to desktop

I had the following problems prior to reinstalling Windows. I am not sure if they have gone away with the reinstall:
- graphical glitch while watching youtube, computer will freeze and restart.
- installers of any sort will fail to complete. They will encounter some error and crash.
- Windows Update will successfully download software, but will run into some error while installing (I had the hunch that with every update I ran, the more frequent system errors occurred)
- graphical glitch in game accompanied by audio glitch. Eventual game crash.
- many random BSODs

I have checked to see that all cords and extensions are firmly in place. I have updated graphics and motherboard components using the cd that came with it as well as from the manufacturer's website. I have run a test on the harddrive. I have run memtest for 10 hours. I have reinstalled windows twice. Anyone able to deduce what the issue is for me?

Specs:
OS: Windows 7 Ultimate 64bit
Motherboard: ECS A960M-M2
CPU: AMD Phenom II X4 965 BE
GPU: ATI Radeon HD 3000
RAM: Patriot Memory DDR3 (2 x 4GB) 1600MHz
Hard Drive: IDE 250GB
PSU: Rosewill 500W ATX12V

Other Notable Details:
- Prior to buying, I confirmed that the ram I wanted to use was compatible with the motherboard. The cpu as well. However, I read something about the cpu I'm using preferring 1333 MHz RAM?
- I am using an HDMI cable to channel video and audio to an HDTV serving as a monitor. Quality is great, but I read on forums that the HDMI connection might be a problem?

 

Next time note on a piece of paper the bsod's code then search for it to identify the problem.

 

there is a chance the dumps get saved, in that case you could try BlueScreenView and find the error codes.

 

Sounds like the hard drive is beginning to fail. Run some tests on your boot drive such as AIDA64, AS SSD, Anvil Drive benchmark, HDDHealth, etc. Something will probably show up. You will be able to see the temperature of the drive and see if it is too slow or has errors.