Virgil,
The Capacitor used with an Alternator for Autos is probably only there to reduce noise which would interfere with the ECM [Electronic Control Module - the on board Computer], or to get rid of the "Dentists' Drill Whining Sounds" that get impressed into the Audio system's Power Amp.
Question: How bad and at what speed does the drive belt slip / squeal?
Did it begin to squeal on the old Alternator, just prior to it's malfunction?
Have you charged the Battery with an AC to DC charger [a normal Battery charger] and if so, does it hold a charge or does it load the charger constantly [looking for shorted cell(s) in the Battery with this question].
I would verify the conditions of the Battery and make sure there's no equipment that is overloading [ignition coil, radio, etc.], then try getting the belt to not squeak [try running the belt over a bar of soap while the engine is at idle. that should get the belt to stop slipping on the pulley].
The slipping belt is indicating a very high load output [unless the belt/pulley assembly is loose or not fitting correctly]. It's trying to produce as much True Power [Wattage] as is requested, and this is derived from the Horse Power of the Gasoline Motor.
Try charging the Battery with it removed from the car's circuitry [disconnect the posts]. Charge it overnight [at least 6 hours] and see if the charge rate remains high or not.
Shorted cell[s] will make a Battery appear to work OK when lightly loaded [radio on, motor running, etc.]. The underlying problem becomes apparent when trying to start the motor. It either cranks very slowly then quits, or just will not crank at all.
Good luck!
Scott SET
