I have a 2001 LaSabre that had a bad LR turn signal out. The bulb was broken and the socket had gotten hot enough to melt it a little.
I replaced the bulb and it worked fine, but now the car will not start.

Charge the battery and test.

Yes. It was the battery. It'* a Delco that has been in for over 7 years. Have never had trouble starting before, but had the trunk open for a while and the trunk light was enough to draw it down to 9 volts.

7 years is magical....

The owner told me it had been in there for 35 to 40 years, but he is in his 80s and a bit forgetful. His wife said not that long, but more than 7 years.
Do you know of any way to turn the headlights off when the car is running? I found nothing in the manual and I don't think there is a way.

I believe that is standard and I don't think it'* legal to delete it.

Press the button with the lamp symbol on it to turn on the headlamps. Press it again to turn them off.

When the headlamps are turned on, the instrument panel lights and the parking lamps will also come on

If you have the Twilight Sentinel, slider button, pressing down and releasing should also turn them off while running.

The lamp symbol button only works when the car is off and the Twilight Sentinel slider controls how long the headlights stay on after you turn off the car.

While running in park, my sentinel horizontal slider is a bit different, but does allow me to turn off the headlights while running, by forcing slider all the way left and release. May have to do it a couple of times to force them off.
In the owners manual your vertical slider appears to have a bit of room yet, to try to continue to push down further a tad. Are you able to push it down further and release, for it to work then?