Are the wires reversed? Yellow should be constant and red should be ignition source power. Although I don't know if that even matters as far as powering the unit up. Check the fuse on the back of the HU if it has one. Make sure the ground is good. If you tested the wires going directly to ground with the meter then a problem there wouldn't show. Run a continuity test on the ground wire.

 

You already tested 12v on your Battery and Ignition lines so you should be good there, water damage commonly will blow a fuse in the vehicle.
Check ground, or make a new one.
Headunit Fuse (if applicable)
Rule out a Short: Only connect the Battery, Ignition, and Ground (no speakers or remotes).

If none of those work I would suspect the wiring. At that point I would remove the radio and harness to test with a power supply outside the jeep.

If you had Ingition and Battery wires swapped, the unit would power up when the ignition is on, but go off soon as you cut ignition and lose the time/stations etc.

 

So last night I played with this some more. First try as previously wired up the radio came on for 2 seconds and turned off. I tried checking all of my wiring for loose connections, and was able to one more time get the radio on for a few seconds and then it cut off. I finally pulled the unit and ran a long run of wire to the battery for both power and ground and the head unit still did not turn on.

I think I may have a bad unit I'm returning it and going to try a new one. This time I'm going with a pioneer instead of the cheapo Dual unit I bought originally.

 

My HU won't turn on unless the yellow wire has 12 volts as well as the red. You may want to try that first.

 

Thanks, that is exactly what I tried. Powered them both straight off the battery together.

 

Okay. Wasn't sure the way it was worded.

 

New head unit arived yesterday, and installed with no issues. I now have tunes.

 

Good deal.