Trust me, if it was a memory problem, you'd have no worries - memory is so cheap these days, its amazing!
Think about it this way - if you have a motherboard problem, meaning a new one is required, someone will need to take your machine apart and fit a new one - the motherboard is basically like a car's engine.
It will cost far too much to replace it, if the machine is not under warranty.
For the cost of buying a new motherboard and getting someone to fit it and have your machine up and running, you could easily buy a very decent brand new machine.
If your laptop is out of warranty, then that tells it's well over a year in age - bite the bullet and look into getting a new machine.