Obtain access to an inexpensive digital voltmeter. Every home garage toolbox should have a least a $15 Radio Shack digital volt/ohm/ammeter and a $3 car battery test light.
Measure voltage at the car battery expecting 12.6 volts with engine and lights off, key out. Much less than +12.6v, the battery is likely bad and won't take a complete charge or isn't getting a proper charge. Then start the car and expect +14.4 volts at high idle. Much more and the regulator is bad, much less and the regulator is bad. A well working regulator will stabilize the charging voltage to 14.2 to 14.6 but can drop to 13.6 at low idle of if battery is overcharged or the headlights are on with heavy current draw on the battery.
Alternators have 3 phases AC and when 1 phase goes out, it isn't enough to be sensed by the car'* computer but enough to give such early warning signs. The can definitively be measured with the meter at only 13.6v battery at high idle.
Your problem can be poor battery post connection as other allude to (cross fingers) but also can be early signs of alternator diode regulator problem...the whining is the alternator clue and your voltage diagnosis will confirm the rest.