I have a Chrysler 2002 T & C. When the ignition is “on”, everything works, but if the car starts, these accessories drop out and don’t come back on for minutes at a time. The ignition switch has been replaced, but it still happens???
Check to see if power is getting to the fuses for those things using a test light probe or meter. If there is power there then there is a wire problem after the fuses. If there isn’t any power to the fuses the trouble will be before the fuse and after the ignition switch.
To add to Cougar’s list, I would suggest the same thing except rather than power check for ground. (Note follow up on Cougar’s list first.)
When you had the ignition replaced, sis they also change the electronics that bolt to the back of it? in all the switches I’ve seen, the actual switch is a small plastic assembly mounted on the (metal, mechanical) ignition switch. If it’s that part that’s not switching things on/off properly, then the problem can still be with the switch.
I would say to do Cougar’s and Joseph’s tests first, though, to rule out the other items.