Yea.. sounds like the logic board... but it's POSSIBLE, it could be the top case. The top case has the power button... and I've seen cases where (pun intended) a water spill has caused damage to the top case... and no one can get the computer on because of a damaged power button.
But, more than likely, it sounds like the logic board. If you have no other damage to the computer, you can have Apple send it into their repair depot for a flat rate repair fee of about $325. But remember, they don't guarantee your data. Being that the 867 is about 4 years old... I would say it's probably about time for a new one anyway.
If you're interested in selling the broken computer... I'd be interested. If you need me to remove the hard drive and get your data, or send you the hard drive so you can retrieve the data or, send you the hard drive with an enclosure so it's like an external hard drive and you can retrieve your data from it... I can do those things too.