First off, have the old capacitors been replaced on this machine yet? If not, then that's a good starting point and replace all of them as all of those caps will go eventually.
Besides that this is an interesting one since you can hear the games playing but have a blue screen. This may be an issue with the contrast wheel. I'm sure you've tried adjusting the wheel several times. Have you tried adjusting the wheel and looking at the system at an extreme angle at say about 135° or so? If you can see any kind of a picture at this angle, than I'm fairly positive it's a cap replacement issue. If not, then I would next check the contrast wheel and the solder points. See if the points have lifted, poor soldering or too much solder (cold joint) and even take a can of air to underneath the wheel and electrical.
That's the best I can suggest for now. Hope this helps.