I also want to accomplish this Dave. The beat I can figure is I have to find out what kind of button it is, remove the button and solder one in its place. I am setting up a Intel Nuc 3 inside a NES (like DaOldMans Pi-tendo) and I want the Nintendo power button to operate the NUC itself. If I had better soldering skills I would risk it but as of right now I am in limbo until I can find someone who will fo it for me.
I dont know if you can modify that NES power button to be a momentary button (you might be able to), but another alternative is to find another set of buttons and unsolder the reset button from the second set and unsolder the power button from the first set. Then solder the reset button back onto the first set. Again, Im not sure, but it looks like the caps might pry off, so you can swap the old power button cap with the new reset cap. You then will have power and reset labels with both buttons momentary.
Another option is to rig up a small momentary button and glue the power cap on to it.
Im interested to see what you will do.
It would be neat to have power and reset buttons both work, since it will be easy to hook both to that board.
If you need someone to solder it, send me all the parts and I will do it for you. (not real sure about adding a different type button though as in last option, that would take some serious planning).
One other option is to use a capacitor to supply a pulse when you switch on the power button, but this may be a problem when turning the computer off, unless you be sure to turn off power button before shutting down.