I blue screen error means something happened that is so bad that it can't continue. The error is logged in the Event Viewer, so you can check there for the error code. Googling those error codes don't always reveal the cause but at least you can try to see what it is trying to tell you. Example: It could be a IRQ_Less_then type of error which would tell you that it's likely a RAM error.
You can download a Blue Screen Viewer program that will help you to decode the failing program or module at the time of the crash from a company called Nirsoft (it's free). Again..it might not be much help because in my experience the failing program or module is usually a common Windows process which is not the problem. it's just usually getting caught up in the crash but not the cause of the crash.
Due to the age of the machine the first thing I would look at is cleaning dust/dirt/ off the fans inside. With the power unplugged I would remove all the RAM sticks and then put them back (this is called reseating). Make sure to press firmly when you put them back, and that the RAM retention clips are engaged (they hold the RAM down). You could also make a bootable USB ram test from a program called> Memtest (Passmark software-free). After you run it for 4 passes (that will take hours) it will test all the RAM with different patterns. I suspect you will see red errors right away if you run that test and you have bad RAM.
If you still have a problem then you need someone who can swap known-good parts in and out to find your bad part. You could have a failing video card or a bad power supply etc..