Need more specifics. Is the starter motor cranking the engine over but it just won't fire up? Or is it turning over very slowly? Or is the solenoid clicking, but the engine won't turn over? Or is there no noise at all? A majority of electrical issues are the result of poor or corroded grounds, so it never hurts to check them and verify satisfactory condition. The voltage regulator isn't directly involved in starting the engine. The engine could be started and run briefly with no alternator or regulator present provided the battery was sufficiently charged. The fact that the regulator is heating up May be a separate, unrelated issue.