yes, low voltage will cause a problem, so replace the alt or see if NAPA has a stud for it.
Also, has the ign switch ever been replaced /new one under the Recall?
if not, read this;
AUTOPEDIA™: Ford Announces Largest Recall
Do you have a CEL?
if so, check for codes
EEC-IV Self Test & Connector Location & pics, Bronco & Ford by Ryan M
www.fordfuelinjection.com ? How To Run a Self-Test
or got to AutoZone for a free check and come back here w/info
Charging V is one of the basic no-run troubleshooting checks; read this;
TS basics are;
Ignition is is EZiest - pull off a plug wire & check for spark while cranking engine; use a rag to insulate yourself from the high V; watch fingers near fan
Fuel; when turning to start, do you hear the electric fuel pump whirl?
could use a fuel pressure check at Schrader valve on fuel rail
or pull a plug after cranking to see if it is wet w/gas; etc.
Did you replace the TFI module?
and the Hall-effect sender & it's connector, if bad (commonly called "pick-up) a inside the distributor?
if not, read this, for "Stangs" but similar.
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