First off, if you're not sure what you're doing, I'd advise against opening up your computer. If you do open up your PC, understand that you are doing it at your own risk and we can't be held responsible if bad stuff happens.
VGA stands for Video Graphics Adapter, and is simply the circuit board that controls the display. If you look inside your computer, the monitor is almost always plugged into the display adapter. On some lower end machines, the video adapter is integrated into the motherboard (the large square board at the back of the case), in which case, you probably would need to replace the entire motherboard.
If it's the memory that is a problem, the memory may need to be re-seated or replaced. I don't know what sort of memory is in your computer, but you may have one or more "sticks" plugged into the motherboard, usually located near the CPU (the large chip with a large heatsink and fan attached).
In any case, you may also want to use some compressed air to evict any dust bunnies from your system. This allows air to circulate more effectively, preventing the system from overheating