ask a room full of chef's how to cook an egg and you'll get 12 different answers. As I too am a computer tech, and after reading the posts above, I shall tell you how I would cook this egg.
Is it a memory thing? It's possible. Lack of memory? Most likely not, but still possible. There could be a portion of the memory that is bad, and when it gets written to, the computer freaks out and crashes.
Imagine a square. Now divide that square into 10 squares across and down. Now you have a square with 100 squares in it. That is what your memory is like, just many more squares than 100. when your computer uses the memory it will usually just stick it anywhere there is room. It does not start at the first square, fill it up, and move to the next. It may fill square 55 and then 82 and then 5 and then 77, until it is finished putting into memory what it needed to put. Maybe of all the squares on there, square 43 in faulty for some reason. The computer is going along, filling in squares and decides to use square 43 and {{CRASH}}.
Replacing memory is cheap and it is fairly simple to do. There are other things you can try in the meantime. I don't feel comfortable going into detail about these on the open forum as I will not be responsible for someone being adventurous and ultimately hosing their otherwise stable computer.
Things I will recommend would be this. Clean your computers hard drive of all temp files, temorary internet files, and other junk. I have a program I have used for years that is very reliable and it is very thorough. It is called
Window Washer. It washes things that a normal user wouldn't be able to wash. You would have Temp internet files (TIF) for Internet Explorer and for Firefox and any other browser you may use. They do not use the same TIF folder.
Of course, like Rockmower suggested, run a virus scan. A thorough or deep scan. This may take a bit of time but it will be much better than a "quick scan".
Like I said though, there are other things I do when I get called to someone's house to fix their computer but they are a bit more involved and shouldn't be "put out there" for just anyone to try. If you want, you can PM me and I can go over them with you, but honestly, from what I have been reading here, I would suggest you start by replacing your memory. Mind you, I am only reading the problem here and am not there to see first hand what it is doing and therefore I am only making assuptions from the information provided.
If you wind up replacing your memory, be sure to go someplace where you feel they would be knowledgeable. Computers can only handle up to a certain amount of memory. After that, they don't "see" it and you've wasted your money and may have potentially created a new problem. Also, ask the salesperson what the name brands are for memory. The most reliable and oldest name out there. Do not try and go cheap. This is an important part of the computer and you do not want to put any old part in your computer. There is the old saying, "you get what you paid for". This holds true in this case.
Good luck, break a leg, may the force be with you, and all that good stuff.