I don't believe the IM being on or off or the User Interface buttons being pressed are actually relevant, probably just coincidental.

The clicking would be my first concern. The overload or relay could be bad and not allowing the compressor to start but from history of these units I'd guess the main board is the issue.

Before you spend any cash on other parts, pull it out, unplug it and pull off the main board cover. Wait 15 minutes, then plug it back in and try to determine if you are hearing a relay on the board click or the overload open.
If pressure differential between high and low side is high (head pressure) that overload stops the compressor from trying to start, after a few minutes it cools and resets and tries again. It may do this several times before allowing the comp to start. But usually within 30 minutes of compressor off the high/low side pressures will have equalized and that overload is no longer unhappy. Your condenser fan next to compressor will probably also try to start so watch your fingers.

If the clicking is from your board you probably need a new main board, not uncommon at all and GE has made a single model that replaces several older ones, including yours.

So try to narrow down what you are hearing before you throw money at it.

GE WR55X10942P Control Board - AppliancePartsPros.com