Yes, it turns on and run perfectly, and the battery is charging normally. I have tried ungrounded and grounded AC-plug, but no differens. A friend has the same problem, he has a smaller computer 13" or 15", I have the 17" model.
I solved the problem, but I don't know how. I opened the computer, cleaned it up (it was not so bad after almost 5 years!), disassembled the keyboard and touch pad, cleaned the connectors (already looked clean) and reassembled the computer again. When I restarted the computer, the keyboard and touch pad still did not work. After reseting the PRAM (or what they call it?) by hold the start button for ten seconds (begin with computer off) they both worked again.