Computer help forum: How to find out what's wrong with my computer?

Here is my computer with all the specs and info- http://h10025.www1.hp.com/ewfrf/wc/document?docname=c01949110&lc=en&dlc=en&cc=us&product=4107708
Excuse me for not posting all the info right away, But that was my first post and I wasn't sure if this is the type of place where questions like mine go unanswered (cough XDA). But thanks for the fast reply, I hope you can help.
My computer crashes are almost ALWAYS while watching a youtube video. The chance of it crashing is greater when the video is being played in full screen or at any resolution greater than 480p. It does occasionally crash at other times too, but no matter what it is always while using the internet, like when doing normal browsing. In fact, I was typing this reply out earlier on this computer hoping to god it wouldn't crash, but it did and I lost all my progress. But pretty much, if Google Chrome is not open I can rest pretty sure that it's not going to crash. Upon crashing, it displays a weird morphed, flickering image of whatever was last showing on the screen. I have some photos if they would help?

A few months ago, we were having some pretty bad thunderstorms in our area and this computer went through 2 power failures in a short amount of time. One was as I was sitting here using it, and the other was while I was away and the computer was in sleep mode. Could that have caused problems?
I recently removed the CPU fan and heatsink, and blew out all the dust and wiped the blades. I did my best to not scrape off any of the thermal paste and put it back exactly where I removed it from. But one foolish move that I made was that I put the fan on backwards, and it remained that way for about a month before I flipped it around. In that time the computer was very loud.
I have done some messing around with the internals before, but nothing too crazy. I've just removed the fan and heatsink, removed the ram, and that's about it. I've put everything back precisely where it originally was though. Also, I have added 2 things. I put in an older 180 GB hard drive where I store music, and one single fan toward the back of the computer. Altogether, I don't believe I have damaged any of the parts in there at all. I have run the Hardware Diagnostic tools and there is never a problem to register with the software, even under stress tests on every piece of hardware in there. Also, it's weird that the computer doesn't falter while undergoing a stress test, yet while simply browsing the internet it crashed dang near every time.
Another thing, I have AVG free version 2013, and have run full computer scans without any virus threats. I'm very cautios about viruses. AVG pc tuneup also has been run, and it defragmented my hard drive to great condition and overall increased speed a little.
I will download and run those programs you linked right away, and have the results when they're finished.

First, whenever you remove the heatsink fan from the processor, you MUST scrape OFF all the old thermal paste, and reapply a thin coating of new paste.. If you don't, overheating and freezing, especially when watching/playing videos is a high probability..

Second, since the problem is also happening with Youtube/Flash videos, please try turning of the hardware acceleration for Flash per the instructions below:

first, check if you can see the Flash animation (banner) without the system crashing at:
http://www.adobe.com/software/flash/about/

Don't worry, it's not a video, it shouldn't crash -- if it does, this won't fix your issue. If it works without crashing, right-click on the Flash animation (banner) and uncheck "Enable hardware acceleration" from the Settings panel. You should now be able to view the YouTube videos without crashing the computer.

And on Windows 7 computers, some folks are finding relief for your issue in Internet Explorer, by opening the Control Panel-Internet Options-Advanced tab.. Once there, place a CHECK mark in the box next to "Use software rendering instead of GPU rendering", then click on "apply", then OK.

Hope this helps.

Grif

I ran the anti malware/ spyware programs and some bad things did turn up, they are gone now though. I'll be sure to run those every now and then to keep things clean in there.

I'll try to get some thermal paste as soon as possible and get it in there, I had always felt like that was a contributor to the problem.

My computer stayed alive through the flash animation and the hardware acceleration is now disabled. Also checked the use software rendering instead. Hopefully this gets rid of the problem or at least lessens it.

Also what would your thoughts be on putting a graphics card in this computer for some casual gaming? What is the best kind that I could successfully install here? I want to eventually build a computer from scratch but would like to get some practice with this thing while it's still usable.

Thanks for the help man, Very very much appreciated

The link you posted indicates "Also supports PCI Express x16 graphics cards" so if you're considering gaming on that machine, it would certainly help but since that particular processor is only a 2.8 Ghz setup and the memory installed appears to only be 3 GB. Since you've got a 64 bit version of Windows 7, you'll want to upgrade that to the max but it's a little unclear, using the link you provided, as to who much the motherboard would support of DDR3 RAM. Even with the upgrade of memory and stand-alone video card, you'll still be cramped with the slower processor. But it should get the job done, just not perfectly.

Lots of graphics cards will fit the bill and much depends on the amount of money you want to spend.. I'm not really a gamer and as such, you might want other recommendations for top-end or even less expensive video cards.

Hope this helps.

Grif