Look at all of your cables (especially the keyboard ribbon cable) and make sure that there are no '''tears''' in them. They could be so small that you can hardly see them, but it could be causing the problem.
The power button is connected to the logic board through that keyboard ribbon, so it would be very important to check it and its connection again. I am skeptical about that connection of yours. It should quite obviously slide into the connector and then lock down with the bracket. You shouldn't be able to pull the ribbon out when the bracket is locked down.
If it still doesn't seem to be working, if you have the means, you could theoretically extract the hard drive, boot another Mac from it, and set it to schedule a boot-up at a certain time. Then, when you place your hard drive back into your MacBook Pro, it should ''turn on by itself at that scheduled time without needing the press of the power button'', and you can see for yourself whether the keyboard connection is good or not. Does that make sense? If you want to try this method, let me know if you'd like more detailed instructions.
By the sounds of it, though, your logic board should be just fine if you were careful enough. It's the keyboard ribbon cable that's getting me. Also, based on the other functions of the MacBook Pro, it sounds quite hopeful and probable that your logic board does still work.
Good luck with this! I have faith that this will be solved without the replacement of your logic board!