Starter gear doesn't move up to engage flywheel gear when started

The solenoid does two things -- it closes an electrical contact to run the starter motor, and also pulls a lever to slide the motor gear up to engage the flywheel. Since the contact is closing, the solenoid itself must be OK, but the lever could be broken, or the sliding gear could be binding or stripped. Since you're looking at a probable replacement, try cleaning with compressed air, then squirting some WD-40 into the starter gear area - you could get lucky! Otherwise, you can replace the starter/solenoid assembly -- you can find replacements on eBay for about $80. Less expensive but more time consuming is to remove the assembly, disassemble, and replace just the defective parts if you can find them. Good luck! Please rate my answer if helpful, thanks.