I had to fix the exact same thing on one of my HP500's. I am sorry to hear you are having issues getting the drive back on, but honestly, this is why I didnt mess with the drive at all.

There is an alignment tool you'll need to get the splines lined up with the motor. But maybe there is something else that needs to be done.... I am a novice when it comes to pulling drives on boats.

You need to check the alignment of the engine before installing the drive. You can get a tool from any Mercury Marine dealer, sorry I am at the house and don't have the Part number with me. Any decent sized dealer should have one in stock and they are around 100 bucks. Even if you did not adjust the mounts things could have changed when you bolted the engine back in or it may have been off to begin with. I am going to assume you are running a bravo drive. When you go to install it you should pull the shift link all the way out with a pair of needle nose pliers of it isn't all ready, it should have popped out when you pulled the drive off. Make sure the shifter in the boat is in the neutral position. Lightly clamp a pair of vice grips on to the prop shaft so that you can turn it easily while inserting the input shaft through the gimbal bearing and into the coupler, this will align the splines and allow it to slide in. Just make sure that the shift link closes around the shift cable end properly and it will push the link in and the drive will end up in neutral. Then just install the nuts, the trim cylinders and the speedo connector if yours has one. God luck, any other questions just let us know.

Yes aligning the motor is inportant but when you check that it also realigns the gimbal bearing with the coupler to let the input shaft go in.