I drive a 2004 3500 cummins automatic. i just recently bought the truck and i have experince no throttle response after stopping or when going at speeds under 30mph. it will just idle at normal rpm's and i have to tap on the throtle a good 4 or 5 times before it catches. but once it happens the engine light comes on but doesnt stay on long enough for me to take it in and read it.it was only happening once a week but now it seems like its almost everytime i get in the truck. also when it gets close to 40 degrees out side the truck wont start until it warms up to about 60. i replaced the heater on top of the fuel filter but still no change. im not sure if these two issues have anything to do with each other. the truck is bone stock. i want to mod it but i wanna make sure all my kinks are worked out before hand. im in the military so i have very limited time to tear things apart to trouble shoot. the lift pump has been changed out a few times by previous owner( my grandfather)

 

Test the intake air heater. As for the throttle, your tps is mounted under the driver side battery tray. You can remove it to test or if you have access to a scan tool you can watch tps percent and volts to determine if you have problem with it.