Have you changed the solenoid yet? Relays involved might need replacement. How old are the battery cables?
I'm not sure whether on your car your voltage regulator is a separate unit from the alternator, but if it is separate, change it. Somewhere along the line they became an integral unit.
Is your battery charging? When you try to start it, what is the voltage range of your battery as you check with your voltmeter?
Coincidentally, how old is the starter?