I had the same problem with my 50HP 1998 Johnson outboard trim and tilt. What I found, after removing the trim and tilt electric motor, was that the brush holders and brushes had gummed up to the point where the brushes were seized up and no longer making contact with the armature's commutator. Fixing this problem is rather simple. Before starting, note that it could be wise to obtain a few inexpensive parts that may need replacement: the large O-ring between the tilt motor base plate and reservoir housing, and new motor brush springs. Even without these parts, you can at least do a temporary though effective repair if you need use of the boat right away, and I'll explain how.
To get started, first you need to loosen the small pressure relief screw, to left of the larger drain plug screw on the tilt/trim fluid reservoir base. Loosen about 2 and 1/2 turns. Then you can manually tilt the engine up and engage the locking lever to keep the engine raised.
You should be doing this with the boat out of the water and on a trailer on dry ground. Lay out a drop cloth on ground, beneath the tilt/trim unit to catch any screw that might fall when removing the tilt/trim motor, as you probably will drop one and it will be almost impossible to find without the drop cloth in place. Looking at the tilt/trim motor housing, you will notice that there are three small screws which fasten the housing to the base plate, and 4 larger phillips head screws that fasten the base plate to the fluid reservoir. You want to remove the 4 large screws. Getting at the two screws behind the tilt/trim motor is the hard part with the engine attached to the boat, but it is made relatively easy by using an appropriate tool. I used a 3/8 inch drive socket with a driver extension, fitted to a socket of the correct size to insert a large phillips head drive bit. To prevent the drive bit from falling out of the socket, I used a dab of silicone sealant inside the socket before inserting the drive bit. Here's a photo of the tool I used:
This tool would have been better suited for the job if it had been a quarter inch shorter. I had to lift the engine a bit more, to gain clearance, by placing a wedge under the locking lever. For each of the 2 large screws behind the tilt/trim motor, apply a dab of silicone sealant to the tip of the phillips driver bit before removing the screws. This will help to prevent removed screws from falling, though you may still have one or both drop. If one or both fall, but don't fall to the drop cloth, use a magnetic pick-up tool to fish them out before attempting to remove the tilt/trim motor from the fluid reservoir, otherwise a screw could fall into the reservoir and be difficult to remove. With all the screws safely removed, you can now lift the tilt/trim motor away from the reservoir housing. It is fitted to the housing snugly, so you will probably have to gently tap against the motor housing a few times before it will budge. Here's a photo showing the underside of the motor, with its baffle and motor shaft pump drive socket in place.
If you don't see the motor shaft pump drive socket as shown in this photo then it will either be found attached to the hydraulic pump, or may have fallen into the fluid reservoir, in which case you will need to find and remove it. You will need to carefully remove the large rubber O-ring that you see here surrounding the round baffle plate. With the tilt/trim motor removed, the pump reservoir is now exposed as shown below, and you should cover the reservoir immediately to prevent any debris or insects from falling into the fluid. Notice that the hydraulic pump's drive shaft, which the drive motor's shaft socket fits over, is shown at the center of the reservoir. I removed fluid so that it would be visible in the photo.
After you cover the reservoir to protect it, you can remove the round baffle plate from the tilt/trim motor base, and you can remove the motor housing and armature from the base plate after removing the three small phillips head screws. Next, remove the brush holders from the base plate, and what you see will look pretty much like the photo shown below. You will notice that there is some rust and corrosion where some water had evidently leaked in past the large O-ring. You'll want to remove the rust and other deposits from the housing and the brush holders, and you can also remove the reddish-brown plate seen here to clean beneath that.
If either or both of the brush holder springs is damaged, they will need to be replaced. For an effective yet temporary repair, until you can obtain the correct springs, either visit the local hardware store or take apart a few ball point pens until you find a similar diameter spring that you can use. I actually cut such a spring in half to get two springs of appropriate length. Notice that the tips of the brushes are curved to fit against the armature's commutator, and when reassembling them into the brush holders you want the curvature to be properly placed. With the base plate ready for reassembly, grasp the tilt/trim motor housing in one hand, as shown below, and pull the armature out of the housing. It will require that you pull ******* the armature, because the housing's field magnets want to keep the armature in place.
With the armature removed, wipe clean the interior of the housing as well as any accumulation on the armature. Lubricate the bearing surfaces at both shaft ends. Clean the commutator with some 400 grit wet-or-dry sanding paper so that it shines as seen above and push the armature back into the motor housing. Now you're ready to reassemble everything. Reattach the motor housing to the base plate, making sure that you hold the brushes into the brush holders, against brush spring tension, to prevent damaging the brushes. The mating surface of the motor housing to base plate, as well as the mating surface of the base plate to pump reservoir, should have a light bead of silicone sealant applied, as we've already seen that without that the unit is prone to some amount of water leakage. Don't tighten the screws fully, as you want to allow the sealant time to cure before doing so. This will give you a better seal. When reinstalling the tilt/trim motor with attached base plate into the pump reservoir, carefully line up the drive socket of the motor shaft with the hexagonal hydraulic pump shaft so that they will come together properly. Since the base plate fits snugly in the reservoir housing, you won't be able to turn the base plate to obtain alignment. Tighten down each of the four large base plate screws slowly and equally to draw the base plate into the reservoir housing evenly, but don't tighten all the way until the silicone sealant cures. Then tighten the 4 large screws and the 3 smaller ones, and you're power tilt should be ready to go after ensuring that the fluid is topped off. Top off the fluid and retighten the screw shown in the first photo before unlocking and letting the engine down with the power tilt. You should raise and lower the power tilt several times to purge air from the system. Air is purged by loosening the smaller screw in photo #1, and then retightening it after you hear the air escape, after which additional fluid should be added with the large upper screw of the reservoir housing removed and then replaced.