Sounds like a weak battery. Not enough CCA to power the starter but enough to allow the radio and some other accessories to power up.
Yea, it is either a weak battery, OR you may get lucky with a free fix. Take your + & - battery terminals off the battery and clean the battery posts with something like steel wool. Get the post to clean metal and then clean the terminal rings. Re-attach, and you may be in luck.
What you describe is usually from the starter (which requires heavy amps to work) not getting enough amperage. This can be a weak battery, but surprisingly it is usually just a dirty connection.
MAC Stainless axle backs & Prochamber
JLT CAI w/ SCT tuner
CDC Classic Chin Spoiler, TruFiber GTS4 Hood
Aeroform Sport Bar (in red to match the interior)
Eibach Pro Springs, 20" Shelby CS69 wheels
SoS Triple pillar gauge pod w/ Aeroforce Interceptor gauges
GT-CS Side scoops
FRPP 4.10 Gears/ FRPP Hot Rod cam