It sounds like the Bendix is bad, or the starter can't spin fast enough to engage the bendix.
The starter has to come out and be tested with a battery. 

I would not want to give up the unique sound of the Y-block starter but that's just me.  Parts are available for the starter like bushings, brushes, stud kit, drive and the commutator can be turned, to an extent. I don't know why the folks who rebuild starters for the local autoparts suppliers couldn't rebuild a simple Y-block starter also. Might be worth asking if all else fails. Soulds like your starter drive may be the problem here. Wish we lived closer, good luck.................

64F100 57FAIRLANE500

I tried jump starting it with another car and had the same result.  It SOUNDS like the gear may be spinning but not popping out.  I also upgraded my engine to body ground wire.  The one that is/was on there was TINY and got hot under a lot of cranking.

I have been toying with the ease and size of the Powermaster Mini-torque starter the last couple days.  Is it a true bolt in?  The wiring is different but I guess there's a way to use the Ford relay.  If I DO wire it to use the Ford relay, can I still use that push button starter remote the same way?  Big post on the left and S terminal?

I'm guessing that cool old Y block Starter sound is gone if I go that route.  

Thanks Miker, that would be cool.  

Lou.  I may take you up on that offer.  

Thanks, gents.

I'm in Milford, CT I might have a used starter......Lou

If you’re in Connecticut, as implied above, there’s a noted Thunderbird restoration gentleman in Southbury. I haven’t talked to him in some time, but I could inquire if it helps. Anybody would know, he would.

miker
55 bird, 32 cabrio F code
Kent, WA
Tucson, AZ

Deyomatic - what state are you located in?

64F100 57FAIRLANE500

Just a thought. Are you sure the connections are good, power and ground? I've had an instance in the past
that gave me that sound and the positive connection at the starter had come loose. 

Located in Harford County Maryland 

Drove the coupe around all day and when I went to fire it up to pull it back in the garage I got just a hiss sound at the starter.   I hooked up my remote push button remote in an attempt to rule out everything behind that, and that's how I was able to hear that the starter itself is making kind of a hissing noise but not actually turning over.  

If it IS the starter...any suggestions on where to source one?  Back about 20 years ago the advice was to find someone that could rebuild the one I had on my old Fairlane.  I doubt I'll find that in Connecticut.  

The solenoid is new as of about 6 months ago.