1997 Ford F-150 Starting Problems

1997 Ford F150 Pickup with 4.6L engine. Lots of miles. Engine was missing and backfiring, but not too badly. Put some additive in fuel, thinking maybe I had some water in fuel, or something. About 10 mi. Later it started loosing power on hills – badly --& wanting to die out. Pulled over to check. Added some higher octane gasoline. Seemed that it was running pretty smoothly at 5,000, or so rpm, but at low rpm it could barely stay running & often did die instead of idle. Tried to cripple home & w/I another couple of miles it died dead in the water – and the starter refused to engage! Wherrring sound only. Took home via wrecker service. Changed out fuel filter. Took starter to local parts store where they checked & double checked starter – checked good. Went back & reinstalled old starter – same thing. Went & bought a reconditioned starter & put it on, thinking surely that would solve problem. Same Wherrring sound anyway. It does, however, engage flywheel, as the cooling fan turns – not very fast – but turns. Battery is good. In fact, had a battery charger hooked up & to “start” position on part of the tests. Can jump across the relay on firewall & I get the same wherrring of starter. Any ideas? There surely could not be any connection between the rough engine problem & starter, could there?