Starting problems 300D

[guage]

I've been fighting a starting problem with my daughters 85 300D.
This has been going on for about two months now.

Every once in awhile (7-8 times) the car well not start after it has been shut off unless I jump start it.
Like the time she drove it to the station to put fuel in it, filled up, went to start it and nothing, jump it and it fired up.

Before I jumped it, the lights came on radio on etc...

I've cleaned the battery terminals ( battery less than 1yr old) the ground cable to the body, cleaned the connection to the starter.

Could this be the starter acting up?
From what I've read in the search, the starters are a bear to change out on these cars.

Any other things to check?

It's at the school now waiting for a jump.