Sporadic Battery charge with Mag AC Adapter

Greetings,

I have a Duo Core 2.0. Bought it on ebay and I would like to repair it. When it arrived I plugged in the Mag charger and it charged the battery fully. I installed Snow Leopard. Then I noticed that the battery would not charge with AC adapter plugged in. I removed battery. Plugged into charger. The computer would not boot.

With the battery installed (now at 67%) the computer will boot. But the AC adapter is not recognized by the computer. The power status icon in menu remains on battery with the AC adapter plugged in.

Also any suggestion regarding safe cleaner for the LCD screen would be welcome.

Thanks in advance.

Curtis