As JBert said check the owner's manual for the fuse locations.
Is the radio completely nonfunctional or does it just not respond to any controls?
You didn't say if you had the standard radio, SYNC, Shaker 500, Shaker 1000, or navigation.
The basic radio system in the dash consists of the control panel, ACM(audio control module)/radio receiver, and the display screen. If you have navigation then it gets much more complicated and the Shaker systems also add amplifiers. There's an APIM, FCIM, and FDIM with those more complicated systems.
I have my doubts that two different radios would be defective in the exact same way though it is possible if it was a common issue. Seeing how this seems like a basic power issue I think that you should check your grounds in the car. If you have bad grounds anywhere one of the first things to go offline is things like the radio and windows. Verify the fuses are good and pushing power thru them with a test light on both sides of the fuse. There's a little hole on each side of the fuse where you can put a test light or multimeter probe. With the ignition on if you aren't getting power thru them then it might be a bad SJB(smart junction box). These are fixable and you can send them out to a module repair service. Automotive Circuit Solutions, Autoecm, Upfix, and Module Master all seem to be reliable module repair services to use. They can test and if needed repair any module.
Here's the wiring diagrams of the audio system:
Ford Workshop Service & Repair Manuals - fordrepair.info - 2011 Mustang 2011 Mustang 130 - audio system and navigation (iihs.net)