Only works on battery but battery still being charged

Hi all,

I'm having a strange issue with a mid-2009 MacBook and was wondering if I could get some ideas as to what could be going on. The symptoms are:

No signs of life with a working 60W magsafe adaptor connected but no battery installed.

When I attempted to power on with a spare working battery and the magsafe connected the system made a short squeal sound (somewhere near the power button for around 250MS) but then powered up. I was able to boot to a 10.6 DVD and do an install without any problems until...

When booting the installed OS I see the desktop for a second then the computer goes into standby. If the computer is woken up everything functions correctly.

Interestingly, even though the computer doesn't boot without a working battery connected and system profiler says that the battery isn't being charged, when I put the spare back into the MacBook it came from, system profiler said it was fully charged so the faulty MacBook must be doing something with it.

The history of this machine is unknown - it's part of an office clear out that I'm involved in; it came to me with no hard drive, battery or adaptor hence the new 10.6 install.

I'd be interested in reviving this machine if it can be done relatively inexpensively; whilst I've never done anything overly complex hardware wise with MacBook’s, I do have a fair bit of experience doing things like LCD and motherboard replacements on pc laptops and having looked at some of the guides for this machine I'm fairly confident I'll be able to replace whatever needs replacing.

Does anyone have any ideas what might be wrong? I'm worried that my limited Mac troubleshooting experience might lead to me wasting money by buying parts that aren't faulty which I'm obviously trying to avoid. Any help at all would be great, even if people feel that it doesn't make financial sense to fix - the eventual plan is to resell once working.

Cheers!