What do you mean you 'have no power'? Pin 6 (pink-red-white wire) of the switch is power to the switch, if you have 12 volts there, you have 'power'.
In Roadsters, fuse 36 feed this as battery power to the switch. In Coupes fuse 6 feeds this but only with the key on. (This is from the 2005 service manual, they moved fuses and feeds around over the four years the car was built.)

The mirror wiring is very simple, it's a fused feed to the switch and the BCM or other modules are not part of it. If you have no power at that pin, I can only guess the fuse was blown during the breaking of the switch or during replacement.

One thing: If you are troubleshooting this without the service manual, you are pretty much wasting your time. You can download the manuals we have (such as they are) here on the forum by clicking here:
https://www.crossfireforum.org/forum...ollection.html