Can I repair problem with power?
Will not turn on with fresh batteries - connections are tight and clean. Power is erratic when adapter is plugged in - the power light comes on and the game plays until just a little jiggle interrupts play then screen goes dark and power light goes out. If I unscrew the back what should I look for?
Take a look at these guides. They will assist you in getting into the device.
2 of the battery terminals are soldered directly to the main board so check they are OK and not cracked/loose. Also check the socket where the power adapter plugs in (if it is an option) on the main board - again check the solder joints aren't cracked/loose