OK, thanks very much everyone, stuck contactor seems to be the most
common suggestion.

The burning smell was before I even got here, so unfortuantely I don't
know where that was coming from (it may have been in her head too, as
she was not certain about it)

My brother came by today (he's a police officer, but use to be in
construction, & has some broad knowledge of home repair and such). He
reset the circuit breakers that were inside the heat pump
itself...turned it back on and everything is going fine so far...

I'm going to leave it on for the weekend while I'm here, and see if the
problem repeats. I plan on turning it off at night, so that nothing
gets damaged when I would be asleep and unaware. (I'm house sitting
for my mom)

I also plan on checking my mom's electicity bills...And thanks for the
info on the tax credit! I was vaguely aware of something like that, as
well as a program here in the state of Oregon I looked into a year ago
for her (since her heat pump was getting old any way)

The house has a wood stove, so heat isn't as critical as it could be.

Again, thanks everyone very much! I'll post if there is any new
information...and please let me know if anyone has any other input
(especially if I'm doing something foolish)