1977 ford f150 with 351 mod, new batt, alternator and solenoid. Turn the key and can hear the click in the solenoid but the starter never turns over? suggestions?

sounds like you have narrowed it down to the starter -- make sure your battery cables are new and connections are good

if the starter is the suspect, before you go buy another one or monkey around with electronics try and use a hot wire to the starter and see if in fact does/does not turn, then go from there

also check if there are any loose wires on the starter, or running to the starter.

make sure that connection from your battery is tight/flush on the starter. sounds like a low battery or bad connect

I would agree with trying to jump the starter, it could have a dead spot in it and you are sitting on it, i have turned them over a little and then had them take off with no load jumping it with my 200 amp charger. if you put it back in it will land on that spot when you need it most.

Could be a resistance in the exciter wire to solinoid. Check voltage at solinoid when turn key to this wire!