Had that same thing happen with my 96 at 146K. I diagnosed it while he was at school and we replaced the starter this afternoon. Wasn't a bad job at all. Mine failed at step 4 and once we removed the starter, we found that the drive gear was always pushed out and wouldn't go back in. I picked up an OEM starter from a '96 Accord w/82K for $25 at the local junkyard. I added my comments in red to the FSM instructions just for clarification.
From the '97 FSM:
Starter Test
NOTE: The air temperature must be between 59 and 100°F (15 and 38°C) before testing.
NOTE: After this test, or any subsequent repair, reset the PCM to clear any codes
Check Starter Engagement
1. Remove No. 33 (15 A) fuse from the under-hood fuse/relay box. (ECU Fuse)
2. With the shift lever in P or N turn the ignition switch to START (III). The starter should crank the engine. If the starter does not crank the engine, go
to step 3.
3. Check the battery, battery positive cable, ground, starter cut relay, and the wire connections for looseness and corrosion. Test again. If the starter still does not crank the engine, go to step 4.
4. Unplug the connector (BLK/WHT wire and solenoid terminal) from the starter (it's the little one that slides off). Make sure the shift lever is in P or N then connect a jumper wire from the battery positive (+) terminal to the solenoid terminal. The starter should crank the engine.
• If the starter still does not crank the engine, remove it, and diagnose its internal problem.
• If the starter cranks the engine, go to step 5.
5. Check the ignition switch.
6. Check the starter cut relay.
7. Check the A/T gear position switch.
8. Check for an open in the WHT/RED wire between the ignition switch and starter cut relay, and check for an open in the BLK/WHT wire between the starter
cut relay and starter.
Check for Wear and Damage
The starter should crank the engine smoothly and steadily. If the starter engages, but cranks the engine erratically, remove it, and inspect the starter drive gear
and torque converter ring gear for damage.
Check the drive gear overrunning clutch for binding or slipping when the armature is rotated with the drive gear held. If damaged, replace the gears.
Check Cranking Voltage and Current Draw
Cranking voltage should be no less than 8.5 volts. Current draw should be no more than 350 amperes. If cranking voltage is too low, or current draw too high,
check for:
• Dead or low battery
• Open circuit in starter armature commutator segments
• Starter armature dragging
• Shorted armature winding
• Excessive drag in engine
Check Cranking rpm
Engine speed during cranking should be above 100 rpm. If speed is too low, check for:
• Loose battery or starter terminals
• Excessively worn starter brushes
• Open circuit in commutator segments
• Dirty or damaged helical spline or drive gear
• Defective drive gear overrunning clutch
Check Starter Disengagement With the shift lever in P or N turn the ignition switch
to "III", and release to "II". The starter drive gear should disengage from the torque converter ring gear when you release the key.
If the drive gear hangs up on the torque converter ring gear, check for:
• Solenoid plunger and switch malfunction
• Dirty drive gear assembly or damaged overrunning
clutch