I have 2 UPSes, both used, and one was marked Working when I bought it
for $7, and the other I might have gotten for free. I can't remember.

Batteries are not cheap of course. A couple webpages gave me the
impression that some people just buy a new UPS instead of replacing the
battery. That's not a sound plan financially, is it???? Surely a UPS
should outlive several batteries, unless there's a lightning strike.

The second question is, I've read the instructions but still not sure if
the second one works. The instructions are short and don't address my
issue

APC XS 900 .

Does there have to be a load for the Online light to go on? It's off.

A 60 watt lightbulb is as good a load as any, right?

OTOH, the Building Wiring Fault light is on, probably because somewhere
I lost the ground connection, but It's only plugged in for testing. Do
I have to plug it in somewhere with a ground to get the Online light to
go on?