1 amp is not enough to power the system reliably.
You did not state that it worked reliably powered up wired throttles.
Also, it's not clear, but you did not state that you tried 2 different radio base stations.
It sounds like you have a "layout id" problem. The earlier NCE wireless equipment can have a layout id of 0 through 3 I believe. This was intended to allow different wireless systems to work near each other, like at a show.
You need the wireless throttles AND the wireless base station all set to the same layout id.
If not, everything else looks normal, but the wireless throttles never communicate and cannot control anything.
Remember you need to set the layout id (I recommend 0) on the throttle with the antenna... I believe the one with the internal antenna is hardwired to zero.
The base station can sometimes change it's layout id... see my web site under the NCE section on how to set the layout id on the base station. Setting the throttles is in the manual.
Regards, Greg