starter problem?

[diesel drinker]

When my 99 7.3 is cold it is hard to start. The starter tries to engage but the gear kicks out immediately. The starter motor still spins. After many tries the starter will engage and away I go with no other problems. I replaced the starter solenoid, on the starter. All I can think of is the starter itself. Can't see it being the solenoid on the passenger fender. Am I correct? Hate to spend $200 needlessly.