Elec woes, crank, no start after running then parked.

Alternator should really have no affect on ignition, unless it's not charging and the battery is "that dead," or it's charging full tilt and you would know that, hot, bubbling, smelly battery, lights very bright and maybe blowing out, etc.

I once had an overcharging problem between Vegas and San Diego, in the military. In the daytime, we drove for many many miles with the alternator intentionally disconnected. (Pulled the connector off the VR)