If you have a battery it'll power the lights until it goes dead. I can't think of a reason offhand that installing LEDs would be harmful to a Univolt converter/charger, they should just be seen as a reduction in load compared to when the lights were on with incandescent bulbs installed.
Do you have a multimeter? If so, what's the voltage at the Univolt output when you're plugged into power, and when not? If there's no change, the Univolt isn't working for one reason or another. Make sure it has 120v power to it (plugged into an outlet with power, all 120v breakers fully in the "On" position, etc.) It may be that your Univolt has simply expired, and a replacement will be a big improvement (once you get past the annoyance of having to set up a new fuse block and an external shunt for the ammeter.)
Il Carriaggio — 1975 Argosy 24 | Il Progetto — 1976 Argosy 28 Center Bath | WBCCI# 15566
He has all of the virtues I dislike and none of the vices I admire. — Sir Winston Churchill