One problem related to transmission not engage has been reported for the 2013 Dodge Ram 1500. The most recently reported issues are listed below.
One day I was backing out of a parking space and when I turned the shift knob on my 8-speed auto transmission v-6 from "reverse" to "drive" the gear would not engage. When I applied my foot to the accelerator the rpm's increased as if I were in neutral. During this occurrence the "d" on the shift knob was blinking. After turning the knob back to park and then back to drive the transmission engaged and I was able to pull away and drive normally. On a different day about 2 weeks later I noticed that while in "drive" and traveling between 15mph and 30mph my transmission seemed to be in the wrong gear. I would apply the accelerator and the rpm's would increase upwards to 2500 - 3500rpms which should not be happening at such low speeds. My truck then began to shutter as it was trying to find the right gear. This truck is a 2013 with less than 1000 miles on it. I have read a similar post on this NHTSA website about this same vehicle. I have also read an article posted on motortrend. Com that references a transmission recall for various 2013 Chrysler vehicles' including the Ram 1500 with 8-speed automatics and a six-cylinder engine. Strangely, when I look up recall notices for this vehicle there is no recall alert for this problem.