It sounds to me like it would be the capacitors on the logic board that are causing the issue. If it has the one button on the logic board and it has a small hole with a bubble coming out of it on the bottom vents then it is the ALS model. You can also put the last 3 digits of your serial number into this website and it will tell you what model you have:
http://www.powerbookmedic.com/identify-mac-serial.php/
The symptoms that you are experiencing sound like the common capacitor issue with these models. You can finds kits that have all the capacitors for the computers so that you can replace all of them at once. The reason that they fail is because of time. It is best to replace all of them even if only a couple look like they have problems. Get back to us with your results.
Hope this Helps