What you might want to do first is to run the extended version of the Apple Hardware Test and see if you get any error codes which might point to what the problem is. This may not be possible if your display is also dark when not playing the game.
There are a couple of possibilities to consider. One is that the graphics chip itself is failing. It is soldered to the logic board, and cannot be removed or cleaned.
Another possibility is that the ball grid array (soldering) that holds the chip to the logic board is failing. If this is the case, you likely won't get an error code with the AHT. However, the ball grid array can be repaired by a specialist.
Since you are bad with hardware, you probably won't want to work on the iBook yourself. However, I have heard good things about DT&T, and I believe that they will do a free diagnosis and give you a price to fix whatever is wrong.
http://www.dttservice.com/index.html
If you want to see what would be involved in working on the iBook yourself, you can check out this site:
http://www.ifixit.com/
You have to decide on your own comfort level with regard to working on your own computer, as it can be very tedious and there is potential to do damage to it. However, this site does give step by step instructions, and you can get an idea of what might be involved should you decide to remove the logic board itself and send it out for repair.
Good luck!