YOu have an 06 - ok, Base, Limited or SRT (there were only like 20 06 SRTs, but I thought I'd ask anyway)?
I ask because Base models have no amplifier but all others do - if you have a Base, you simply need a new radio 'head unit'.

Ok, so the radio is powered up and appears to be more-or-less working.

What about the amplifier? If you have an SRT or Limited (or any 04) model, you have an amp under the passenger footwell. In most model years, Fuse 23 is the "booster" or amplifier fuse; this is fuse 23 in the underhood fuse box on the driver's side. Verify that fuse is not blown. You say you have an 06, most 06s are Limiteds but some are Base or SE - Base and SEs have no amp - the ONLY thing that can be wrong is the head unit - REPLACE IT!

Base Roadsters and Coupes are: Black inside and out, lack power/leather seats, fog lamps, tire monitor, garage door opener, etc.

Next, you need to get under the passenger floor mat, and determine if water has flown under there - destroying the amp. This is common, when the drains under the wipers get plugged with leaves, rain will back up and overflow and get down into the area behind the dash, then run down and get the amp wet. Should the amp not have been wet, it could be the amp died anyway - or it can be that the radio "head unit" has simply failed. You can use a test speaker (any speaker with wires connected to it) to test the head by stripping the ends of wires on teh test speaker and inserting them next to pins of "speaker outputs" on the back of the head to determine if the head is working or not. If it makes the test speaker work, then the amp in the car is the issue.

New aftermarket Kenwood/JVC/etc. heads cost as little as $85 - and are easy to install. Aftermarket amps are reasonably priced from $75 to over $500.