Re: 76 OMC 140 Tilt Trim Clicks
Welcome aboard (almost-a) doc
The tilt package on the old OMCs is a booger. They designed an electric motor that essentially sits at the bottom of a dark, damp bilge ... not so bright. Most likely, you need to pull the tilt motor and have it rebuilt - BUT, getting that beast out can be a real pain. Make sure you have a good charge on your battery before you go ahead and pull it. Also, try supporting your stern drive (or removing it completely), taking off the tilt quadrant (big half-moon lookin' gear) and then see if the drive gear turns at all without a load.
I'm not sure which plate you removed (I'm thinking on the clutch pack at the port side of the stern drive), but those do tend to get water filled - empty, and refill with gear lube. Water doesn't' have a good path to get up to the motor from there. There's worm gear that typically survives pretty well in these old systems, and a hammer coupler that seems to have a 50/50 chance boat to boat.
If it comes to taking the motor off (very common need), you don't need to pull the stern drive or relieve the load on the tilt quadrant. It'll all stay put. There will be two screws/bolts on the motor. They pretty much go all the way through the motor and into the housing. Unplug the motor wires, remove the screws and get ready to catch the motor. Watch that it doesn't come completely apart on you, because those screws hold the housing together. Also, watch that the hammer coupler doesn't jump down the bilge where you can't get it - it sits right between the motor and the worm gear.
If you don't have a good manual - getcha' one. It'll walk you through step by step on this stuff.