[68gmsee]

I've had them chatter when the battery is weak or starter doesn't get enough voltage and I've also had them make the whining sound when the starter bushings are worn. The armature (the part that turns) rubs against the field coils (internal wiring coils) and it won't allow the armature to turn and it just hums.

As you mentioned the ignition should be checked. It has been known to go bad and do weird things electrically but if the starter does the same thing a rebuilder can replace the bushings, solenoid and starter gear. Unless you want to keep the original starter and want to keep it completely stock with original parts, I would just buy the complete starter. Might be cheaper.