OK the cause of this is usually one of the following, in order of likelihood:
1. Bit Rot - Windows suffers from 'bit rot' where it gradually gets less efficient and more and more broken over time. For this reason a lot of people (myself included) will erase everything and reinstall Windows and all needed software every 6 months or sometimes even less.
2. Hard Drive is going bad - Over time, hard drives can develop weak spots in the magnetic storage medium and may have difficulty reading or writing to the drive. This can cause all kinds of strange things to happen, but the most common symptom is the good old blue screen of death at what might seem to be random times. Once 'bad sectors' start appearing on your hard drive, they WILL get worse over time, at an exponential rate, destroying data in the process. Think of bad sectors as being like hard drive cancer... if you find one, its terminal. The drive WILL die, and you should back up all important data ASAP and replace the hard drive. Follow
this link to download Drive Fitness Test. It is the most reliable and easiest to use program I have found for checking your drive for bad sectors. The download is an ISO image so you can burn it to CD using Nero or other burning program. Then boot from the CD (when you start your computer it should have an option to boot from a device other than the hard drive, or it may do it automatically) and run the advanced test. This will do a full read test of the disk surface and is non-destructive. If you get a green screen at the end, wipe the sweat off your brow and relax, because your data will be fine. If you get a red screen, backup important data immediately and replace the hard drive.
3. Overheating - often years of use will result in the CPU heat sink (and graphics card heat sink if it is fan forced) clogging up with dust and losing its cooling capacity. Sometimes fans will seize due to dust, heat and age. Make sure all fans are spinning freely with no rattles, and that heat sinks are relatively free of dust. If clogged, clean them out and test again.
4. Faulty RAM - As with everything, RAM can sometimes go faulty. Often the problem is merely a bad connection. Remove the RAM modules and clean the gold connectors with a normal pencil eraser. Do not touch the connectors with your fingers after cleaning as the oils and acids on your hands can cause a bad connection some time in the future. Re-install the RAM modules, taking care to seat them correctly and the right way around (they are keyed and should only fit one way... people have managed to get them in backwards though so take care). If the problem persists, there are a lot of memory test utilities out there so get one that seems to test very thoroughly as many different bit patterns as possible and try that. A bootable one like the drive fitness test would be best because it leaves as much of the RAM free as possible for testing. If any errors are detected, replace the RAM.
5. Faulty Motherboard - Not really likely, but something I see very often at work due to the poor conditions some of our PCs endure. Overheating can result in some capacitors on the motherboard spewing their guts out and ceasing "capacitating" lol... Have a look at all the capacitors (the little can type things) and make sure theres no goop coming out the the top, and that the tops aren't bulging. If any of them are, this is a sure sign that if the motherboard isn't already dead, its about to be, and the dead capacitors should be replaced, or more likely the whole motherboard.
You'll notice that most of these things can be proven fairly well without replacing anything to "see if it works". This little list is compiled based on the hundreds upon hundreds of PCs to come through our workshop.
Any trouble with any of those testing procedures, just ask! Also if you need any parts, let me know and I can probably send them to you for just the cost of postage.
Good luck!
EDIT: oh and its probably good measure to use the same cleaning process as you used on the RAM on all the other edge connectors... graphics card if its not on-board, any PCI cards, re-seat power and data connectors (unplug and plug in again) etc etc. 99% of the time this process and the list above will solve your problem.