I have a 1979 FLH. The starter spins but it doesn't engage. The starter is fine and the solenoid is fine. I am assuming there is an issue with the starter shaft. Any suggestions?

 

most likely your problem is the starter drive gear

 

Or the starter gear shift lever bent, or ears worn out...either way the outer primary needs to come off.

 

Going with the drive gear myself on this one , hear any kind of hashing noise like it's trying to engage but won't ?

 

There was a hashing sound leading up to this problem. It used to hash a little and then engage. Now it just spins.

 

Drive gear is gone , the clutch rollers inside it took a dump on you . Be sure and disconnect your battery when get into changing it , seen some mangled fingers on guys who didn't . PM me if you need advice on how to , be glad to help .

 

I replaced the starter drive gear. Now it will start, but when I push the starter button it continues to turn over even when the button isn't pushed. I press the button and let go, and it turns over until it starts even when I take my finger off the button. Any ideas?

 

Most likely cause is undercharged or weak battery

 

Make sure your outer primary is aligned good before you tighten her up too. Sometimes you need to "press up" on the lower right part of the primary before tightening. Reason? If the starter shaft throws out and begins to engage, but then sticks because of misalignment, Shovels are made to "spin the starter" anytime that shaft is out. I've seen Shovels sit and burn the starter up or spin it till the battery is dead because of this issue (and because the owner didn't have a screwdriver or wrench to disconnect the battery while the bike was killing itself).

Pretty common on Shovels, and a lot of guys run emergency cutoff switches in-between the positive cable and the solinoid for this very reason.