The outdoor unit running all the time indicates a stuck contactor as
the most likely problem. A new contactor should cost $20 to $30 plus
diagnosis and installation. I can change a contactor in 15 minutes,
and diagnose in in 15 minutes, so you will probably fall under the
minimum labor charge plus parts. It could also be a bad thermostat or
short in the thermostat cable, but those would need fixed anyway if you
replace the unit, so they are not going to make a difference in the
repair or replace discussion.

Whether to replace or not would depend some on her electric bills. If
her electric bills are low, I would fix it. If they are high, a new
high efficiency system (Both indoor & outdoor) may be a good idea even
if it weren't broken. By the way, there is a $300 Federal tax credit
for Energy Star rated high efficiency systems, starting in January
2006.

Stretch