Fixing a 386SX laptop

Hello everyone, My oldest machine is a Goldstar Gold Note 386SX 20 MHz with 2 MB of RAM. I'd like to do many things with it, but no matter what I try to do, at some point the screen starts going dark and then bright and then dark again...varying in brightness until you can't focus on what you are doing anymore. It's a grayscale LCD. Apparently no dead pixels at all. I've been told by someone who fixes motherboards and other things for a living that it's not the screen but something else. However, the man claims he has no time to look into the machine and find the problem. If anyone has any idea of what could be wrong, wether it is possible to fix it and hopefully how, I'm all ears. I will even send it to whoever can fix it and pay for the repairs, like I intended to do with this local gentleman. I'm very curious to at least hear what's wrong.