Since you say this is a NAV radio, I assume that you bought an SRT6 or a Limited model.
Both of these have the Infinity amp under the front of the passenger side foot well.
The base model has no amp, and can be identified by black door handles, windshield surround and black ***** on the radio.

You may have a head unit issue, an amp issue or simply a wiring issue.

Mine did this once and I found that the connection to the door speaker that can be accessed by removing the little pop-out panel at the front of the door was corroded, cleaned it up and has been fine since.