New battery.

All lights on the dash work.

Fuses seem okay.

Stereo works.

Car bump starts.

Key turns and nothing happens: no starter motor or anything. 

Quiet High pitch noise from the engine when ignition is turned on.

Check connection to starter motor solenoid isn't broken.

3 minutes ago, Breezy_Pete said:

Check connection to starter motor solenoid isn't broken.

Will do, thanks. 

Tested alternator and that's fine. The bolts to the air filter are totally corroded so I'm having difficulty gaining access to the starter motor and solenoid. Any suggestions on how to remove rusted bolts?

Removed the air filter & git to the starter motor: all connections are sound.

The is one cluck as it tries to start but still doesn't.  I think it needs a  new starter.