Car Audio Menz, Lend me your ears and your wisdom!

So I've come across and interesting problem.  I have a '96 Honda Civic
EX, a few weeks ago someone jacked my Panasonic headunit (doesn't
matter, it sucked).  It was a clean rip, they cut the wires nice and
clean (at least they were considerate), and they didn't smash my window
or anything.

Now, I've replaced a unit with a JVC, and thus, the aforementioned
"interesting problem".  For some reason, I couldn't get any juice from
the Constant/Battery lead.  The unit would just not power up.  At first
I thought it was defective, but when I plugged my ORIGINAL (stock
honda) radio in (with the stock harness), it also didn't power up,
which leads me to believe that something from the battery --> the
connector for the harness is messed up.  I worked around the problem by
doing something which was probably not the smartest thing to do.  I
have both the red/yellow (ignition 12v and constant lead) connected to
the ignition lead coming out from the car.  The unit powers up, works
great, but it doesn't have any memory, so the clock/presets reset.  I
don't *think* it's going to be a problem, it won't drain the battery
since there's no juice going to the headunit when the keys aren't in
the ignition, but for all I know - my car could shock me and explode
randomly some day. :D

Has anyone come across this problem before?  Any suggestions on what I
should do?

Thanks!