Check your ground where the negative battery cable bolts to the engine block. If that gets rusted/corroded/loose it can cause your issue.
+1 - this is a fast test to help isolate the problem. An upper gear-case that is jacked up will give ya' problems. Doing this test will tell ya' which side of the transom your problem is more likely on....you can remove the outdrive (just far enough to disengage the ball gears) and see if that frees things up.
just be careful of the shift cable while moving the drive around- it's big $