Before pulling the powerhead, make sure the loose connection is not in the brass shift rod connector itself. These screws are often misinstalled/misaligned and stripped. The other possibility is that the find adjustment screw on the shift handle has come loose introducing slop between the shift handle and the horizontal shift shaft.
The problem is that running the engine like this may have caused damage to the clutch dog and gear lugs. But, you will never know until you address the slop in the system, readjust and try again. Good luck, hope it works out.
The only other thing that comes to mind is did someone accidentally/inadvertently remove the little phillips screw that is near the lower lube drain screw on the gearcase? If so, the internal shift linkage probably fell apart and you will probably have to remove the skeg in order to reinstall it properly. But again, if the engine has been run with this issue for any length of time, clutch dog and gear lug damage has probably occurred.
