Bad battery contacts. Try cleaning them with a pencil eraser.
Bad charging circuit. With the Mac ON, there should be a low current DC voltage on the contacts.
Bad battery (they can get old/die just sitting on the dealers shelf). Check its voltage, under a load, if possible. If it's more than 1 volt low, ask for another. Take your meter with you to the shop and see what a 'new' one reads.
Bad plist (/System/Library/PreferencePanes). You can try renaming this, but the OS may not let you. If it does, it will probably want your login password (whether you ever use it or not).
Bad cacheTimeZones cache ( /System/Library/CoreServices). Probably best not to mess with this one...
Always a good trick is to look through the Crash logs. In your Utilities folder should be an app called Console. I think it's pronounced cun•
sole, as it's meant to make you think you will find something in there that will help you find a problem process. Sometimes it does...I'd look at "system.log, /Library/Logs and ~/Library/Logs" at least, then "CrashReporter" (although this is not really a 'crash'). Look in the lists for anything even vaguely involved wit date/time. Report any findings in triplicate,
pink to
Admins,
blue to your dad,
gray for your own records.
Good luck, this message will self-destruct in 5 seconds...4...3...2...1