No power

What's the symptom or problem. The two parts are mot related.

There's a couple of things I can think of. Part of what you described sounds like something is draining the battery while the engine is off. A real common cause of that on Dynastys is too many papers crammed into the glove box. When the door is forced closed, it bends the tab that the light switch is mounted to and the light stays on. That can kill a good battery overnight.

When a battery is nearly completely discharged, it will take 10 to 15 minutes on a charger before it starts to take a charge. That means while the engine might start with a jump-start, if it stalls shortly after that, the battery won't be charged enough yet to restart it.

The easiest way to test the alternator is by measuring battery voltage with an inexpensive digital voltmeter. Before the engine is started, it should measure very near 12.6 volts. If it is closer to 12.0 volts, it is good but discharged.

With the engine running, the voltage must be between 13.75 and 14.75 volts. If it is low, the battery will not fully charge. A common cause is worn brushes in the alternator but those always start out being intermittent. You have to catch that and make the measurement while the problem is occurring meaning the battery light or "check gauges" light will be on and the voltmeter will be reading lower than normal. If that's what you find, the cause can be verified by measuring the voltages on the two smaller wires on the back of the alternator but those measurements must be taken with the engine running.

The map sensor does have the biggest say in how much fuel enters the engine but the stalling problem is more likely just due to the battery being dead. That makes the Engine Computer lose its memory including "minimum throttle". Until it relearns that, it won't know when to be in control of idle speed. You also will not get the nice idle flare-up to 1500 rpm at start-up. To meet the conditions for the relearn to take place, drive at highway speed with the engine warmed up, then coast for at least seven seconds without touching the brake or gas pedals. Until that is done the idle speed will be too low which leads to stalling at stop signs. It will not cause stalling while cruising at a steady speed.