Your car's volt gauge should read about 13.5 to 16 volts with the engine running. It should read 12 volts with the engine off. You mentioned the old battery had a lot of corrosion on the cable connections. Corrosion can cause a voltage drop to the starter, causing it to turn the engine over slowly or not at all. Auto parts stores have testers for batteries. These simulate the load of the starter on the battery and measure whether the battery has enough juice in it. The machine can also test the alternator while it's on the car to determine if it is charging when the engine is running.
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AC DELCO, VOLTAGE REGULATOR -- OEM Design Generator Voltage Regulator, A High Quality Direct Replacement Part Providing Exact Fit For Easy Installation And Reliable Operation.