Multimeter tests. First start the car and check the alt. output voltage (the big wire of the three going to the alt.). A correct reading should be around 13.8 to 14.2 volts. It should have at least battery voltage otherwise you have a bad output wire to the battery.
If it's just showing battery voltage and nothing higher than: unhook both the field field wires going to the alternator (the two smaller push on connectors) then get two jumper wires. Take one of the jumper wires, put it on one of the field terminals at the alternator and the other end of that wire put it on a good engine ground. Take the other jumper wire and connect one end to the other filed terminal, start the car and have the voltmeter hooked up to the alternator output, then take the other end of the last jumper and touch it to the output terminal of the alternator, you then should see the voltmeter go up in voltage quite a bit and hear the engine load down a little. By doing this you are "full fielding" the alternator and putting it in maximum output which you don't want to do for a long time.
If this doesn't make the voltage go above non running battery voltage than the alternator is bad.
Check all leads going to the alternator and regulator as well as make sure the regulator has a good ground. You could unplug the regulator, with the key in the run position the blue wire should have battery voltage and the green wire if still hooked to the field terminals of the alternator should as well have battery voltage.
I know nothing about the voltage regulator you are asking about.