On two different computers I had similar issues lately. In one case it was a hard disk slowly giving up, the problem became increasingly more prominent until the hard disk gave up completely (the faulty area fell in the swap file), a new hard disk fixed the problem. In another case some faulty memory was the problem.

Always run a memory tester when problems are persistent (for Windows Microsoft has a memory tester somewhere on their site, do a search). It might take a while to run a full test but it does eliminate one cause of problems. It is my experience that memory timings may change over time.

In general problems like these can be hard to track down but the culprit is often a broken power supply, a video card problem, a faulty hard disk, faulty memory, a broken CPU, some other broken component, a virus, damaged OS (about the correct order). Remember the broken component might not actually be in use, just loading a driver for it might already cause the problems.

Do a memory test. Next unplug everything that isn't absolutely required (printer and all other external components), also take out all extra hard disks and only use the minimal amount of memory. If you still have problems you'll have to find somebody with some spare parts and start swapping until you have a stable system (continue swapping until you have eliminated all but one cause).