Your radio is an RA1 3.0 Nontouchscreen, no Bluetooth radio , it's really easy to remove .
Two #25 tq screws up top.in the business card holder under the litle rubber mat . Once those two are removed pull straight out with both hands in the card holder only about an inch then gently work the bezel free ( it's just plastic snap plugs ) once you have the bezel off disconnect the electrical connectors and lay the bezel assy to the side . Now 4ea 7 or 8 mm head screws on the 4 corners of the radio . Next pull the radio straight out . Disconnect the mustard colored plug (XM) , white plug AM/FM ,grey MINI USB to the media hub in your console now the main disconnect ( depress lock and pull the handle out and to the left , your done . Sounds dificult to explain but this takes less than three minutes !
It's likely something wrong internally with your radio ...
I have my old RA1 3.0 I removed from my 2014 truck , it's like Brand new ! I'll sale it to ya for $75.00 if you are interested, I upgraded to the RA2 5.0 touchscreen Bluetooth radio with back up cam a while back ...
I actually have an extra RA2 5.0 TOUCHSCREEN BLUETOOTH RADIO That would be plug and play in your 2013 truck if your interested in that one I just posted it in the for sale section ...it's a 10 min job to swap out and upgrade to the touchscreen Bluetooth and back up cam capable radio ...20 min max ! Even if you've never removed your radio bezel .