Update on, "Help! My 2004, Lincoln Town Car seems to be having an electrical problem related to the battery!" D:

Update below, "I have a 2004, Lincoln town car. The first issue I came
across was when I left the light on accidentally, and it drained my battery to
the point that I could not start the car. It could be jump started. The
mechanic determined that it was a bad alternator combined with a bad
battery. We self installed a new alternator (it read 13.8 volts as opposed to
the 12.8 the old one displayed) and a new battery (which had 750 amps as
opposed to the 700 amps the old one had). The check engine light went off,
as did the red battery light. The issues went away for about 3 days and now
the same symptoms are back: The car won't start, the check engine light is
on, and the red battery light is on. Some of the smaller electrical functions
inside the car work fine for a short time but only if the car is parked. They
don't work when the car is being driven. There does not appear to be any
corrosion on the battery cables."
Update:
I have one new development with the car. It started fine this morning. I took
it for a test drive around my block. The steering became very stiff and the
orange "swerving car" icon blinked on
(for the Stability Control System/Traction Control)
along with the (ESP) icon. The lights also turned off and even though their
switch was on, they would erratically turn on and off. I will definitely still
check the battery cable that runs under the fuse box. Thanks Bob Beaman.
:)