|The 3 beeps often means, that the first 64 KByte of internal (processor) memory are not accessable.|
This could mean, the processor is corrupt.
But when you say, after several tries, it's running normal up to a blue screen during a computer session, I guess, it's a thermal problem.
In that case, often the heatsink if full of dust as well as the fan, mounted onto the heatsink.
So you have to clean both and it should normally work normal.
The original poster should always write the last response !!!
Let us know, if the problem is solved !!!