Don't forget about heat. If your computer is shutting down or crashing randomly, open the case and check if the fans are caked with dust. Blow it out with a can of compressed air. Overheating causes a shocking number of 'mystery' problems.

Definitely back up your important files before trying any fixes. I learned this the hard way when I lost 3 years of photos trying to fix a simple problem. Get an external hard drive or burn DVDs of your important stuff first.

I'd check Device Manager for any yellow exclamation marks. That's Windows telling you a driver is missing or broken. Right-click My Computer, Properties, Hardware tab, Device Manager. Fix anything with a yellow mark and a lot of weird problems clear up.

This is a case where spending a little more upfront saves you money in the long run. Cheap hardware fails faster and costs more to replace. Buy quality components from reputable brands and they'll last years longer.

Make sure you have the latest drivers from the actual manufacturer's website, not whatever Windows Update gives you. Video card drivers especially — nVidia and ATI release new ones every month and they make a real difference.