You may have other problems but at the very least you will need to put the cluster back in so that the alternator will charge and the A/C control head will see the voltage at the D+ wire on the alternator and energize the compressor. Back in the day we used and "a/c delay relay" to pull the compressor on 10 seconds after it saw the D+ hot up the alternator. That feature is built into the control heads now but it still needs to see that signal and that signal comes through the instrument cluster. Hook it all back up properly and see if it works, if not then you have yet another problem.

Mark

With the engine running you should have 12 volts at one of the ac pressure sensor plug pins. If you do then shorting the pins together should activate the compressor clutch. If the clutch doesn't energize try connecting 12 volts from the battery directly to the clutch wire. That should make it engage.