Low voltage at constant and igntion wires

1996 Jeep Cherokee Laredo

Been having problems with my girlfriend's jeep for awhile.
The deck worked for a week then started working sometimes, now doesn't work at all. I got out the tester today and the 12v constant wire tested at only 9.65v. The Ignition wire tested at 9.55v.

This has to be my problem, right?
What do you think would cause the voltage to be so low?
I tested the battery and it looks good.

I measured DC volts across the battery terminals and got only 10 volts. Does this mean the battery is failing?
The vehicle runs and drives just fine.

disconnect everything from the battery and fully rechage it. Let it sit for an hour or two. If the voltage is much less than say 12.5 V, it's pretty much dead. Oh yea, try putting water in it before you recharge it.