Try booting up a game and looking at the screen from different angles. I've read that over time the electrolytic capacitors on the logic board fail (1), resulting in a change in display contrast. Replacing all the capacitors helps in some cases. The only screen adjustment available that I'm aware of is brightness for the backlight, which doesn't affect contrast/viewing angle.
Also, take the game gear into a dark room and turn it on. If the backlight is functional, you should see at least some light shining through the screen. If not then you have a backlight issue, possibly in addition to the above issue.
1. Sega Game Gear Repair