M-20 pilot reported runway excursion during landing rollout.

Narrative

I broke out of the clouds very near my destination airport; ZZZ; and flew south of the field to descend for landing. As I was descending; I repeatedly attempted to turn on the runway lights by keying UNICOM. I could clearly see the PAPI lights and the ramp to the left of the runway as well as the very well lit sports fields to the right of the runway; but I could not get the runway lights to come on. I made my approach; but preferred not to land on the unlit runway; so I executed a go-around.I made an additional attempt to key on the lights to no avail. In the downwind leg; I heard a pop in my headset as the low voltage light illuminated on the panel. I switched on my backup alternator; switched batteries; and determined I did not want to be airborne without electrical power; so I elected to proceed with the landing in spite of the apparently non-functional runway lights.I carried too much energy into the landing and floated more than is typical. I may have bounced; but ultimately touched down and began braking. I soon realized that my braking authority was poor as the runway was wet. I rolled out all the way to the end of the runway and made a turn toward the taxiway; but the aircraft skidded as I initiated the turn.The aircraft is undamaged and did not leave the pavement; but I felt a substantial bump as the aircraft turned toward the ramp and I believe the tire on the right main gear rolled over a single runway end light.I knew I was carrying too much speed and I should have rejected the landing; but I let my concern about the potential electrical issue push me into forcing the plane onto the ground. I may have better managed both approaches for landing if I had been able to activate the runway lights.