Power button not turning on computer, but will turn it off?

Laptop would not turn on. Light on Magsafe would not light. Replaced magsafe adapter with known good adapter in a known good power outlet. Replaced DC-in board. Light on magsafe only comes on full sometimes. Power button will not turn on computer. If topcase is disconnected, light on magsafe will turn green. Laptop will turn on via the two jumper points next to where the topcase plugs in. Laptop will boot fine and all the keys on the keyboard work. Power button WILL shut off the laptop. Computer will attempt to shut down after a couple minutes. Reset all the energy management settings to not turn off the laptop for any reason. Ran Hardware test (the extensive option. Took an hour or so. Laptop did not shut off) Hardware test checked out fine. Behavior is the same with or without the battery.

I am completely at a loss now. From my view point, everything seems to work on it's own, but not when it is all put together. Could this be a software issue? Is there something that I could be missing? How accurate is the built in Hardware test?

Any help would be great. Thanks.