See if you have a little tiny hole somewhere near the CD player which is where a pin is inserted to manually release the CD if one is stuck. A stuck CD can cause the radio not to work. I used to have the same radio but I don't recall if it has that CD release hole or not.
If you can not get it working and want a replacement for an '04 Rubicon, PM me as I have the OE unit from my '04 Rubicon out and sitting on a shelf in my garage.
And a big welcome to WF DM MKV.