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.

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.

Have you run a full virus scan AND a spyware scan? They're different things. Norton or McAfee for viruses, plus Ad-Aware AND Spybot for spyware. Run all of them. A slow computer is infected until proven otherwise in my experience.

I build computers for a living and can tell you that most of these problems come down to three things: not enough RAM, outdated drivers, or malware. Check those first before spending money on new hardware.

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.