I went down that road and tried replacing the capacitors, but that wasn't the problem. From what I was told on this forum, the capacitors rarely go out and it is usually a mechanical failure. They were right, but I had multiple problems:
Starting from easiest (and most likely) to hardest:
1. Check the battery, it won't run without a good battery. I've heard it's bad to run it without a good battery. I ordered nicad cells with solder tabs for about $1.50 each on Amazon. Don't try soldering normal batteries, they could explode, I'm told. I gently opened my battery pack with a utility knife along the edges. I used a sharp chisel to scrape the connectors off.
2. Check the wires that go from the r/w head to the daughterboard, they can break easily. Mine broke from all of the messing around I was doing with it. Soldering them back is easy, but the wires are not very long and they are very small.
3. Does the motor run? Can you hear it run, but not see the gear turn? The worm gear can sometimes slip on the motor shaft. This also happened to me. I used a very very small amount of super glue on the shaft and that fixed that problem. You can test the motor with the back off of the calculator while holding the battery in.
4. Does the motor not run at all?
Probable Cause: There is a rubber roller that "melts" with age. It gums up everything and makes a mess. See this link for instructions. This requires a more involved dissassembly. You have to remove the plastic gear and clean the goo off. Then, you can use silicon tubing (available from hobby shops and some hardware stores) to replace the roller. Don't try the o-rings, I tried that and it didn't work as well as the silicon tubing. The tubing was about 3mm or 4mm, I can't remember. It's pretty much standard tubing for a model airplane fuel line. The thickness should make it even with the ridge on the gear shaft.
There is also a cam adjustment that is used to set the pressure between the roller and the card (white plastic flathead screw that is pressed in and holds the gear in). After you get the calculator mostly reassembled, Turn the screw back an forth until the card runs through smoothly without slipping and without a stressful whining sound coming from the motor. I used needle nose pliers to turn it because the screw is not in a convenient place to use a screwdriver.
It's black in this picture, because this is an HP-97:
Possible Cause: There are reed switches with small balls (and one wheel) inside the card reader. This requires even more dissassembly. The reeds should be just barely even or a little lower than the plastic housing. The silver flat head screws are the adjustment screws. If you take it apart and look from the side, you will see what I mean. I cleaned the contacts, but they probably didn't need cleaning because they look like gold plated contacts and reeds.
5. If you do all of this and it still fails, then look for the capacitor (Yellow in this picture).
Edited: 23 May 2013, 12:22 p.m. after one or more responses were posted