I recently moved and apparently did not sufficiently bundle up one of my computers. Post-move it wouldn't turn on at all and appeared to have a bad power supply. Replaced the power supply with a brand new one and the symptoms have changed but it still won't turn on.

There's a solid green light on the back of the power supply.
There's a solid green light on the mother board near where the big power supply cable plugs into it (that light was blinking before we replaced the power supply).
If I press the case on switch nothing happens- no fans, no beep, no POST, just nothing.

I've tried swapping aroiund the ram sticks with no change.

Is there anything to try or is it pretty much a guaranteed dead Mobo or processor? And if so is there an easy way to tell which?

Any help would be greatly appreciated.

Try checking the power switch connections where it plugs into the motherboard. They often can come loose when a computer is moved around seeing as they do not clip in or anything. Make sure it is securely on the pins and give it a try. If your not sure where it goes look closely on the motherboard... there is usually a very fine print labeling it.

To add onto what firekid said. Check and reseat all cable connections as any of them could come loose during the move. Also what brand is the computer. This sounds like the problem a lot of emachines T series XP machines have where when the PSU goes it takes the board with it.