I recall reading somewhere that the Asus charger can put out 5 volts, or 11+ volts (11 + is required to charge the prime.) It could be that it is charging your phone because it is supplying the 5volts, but it may have something wrong with it and it is not putting out the 11+ volts required to charge the Prime.
My first Prime had this EXACT problem where it would no longer charge, and I returned it for a second one while under the return window- I believe the Asus chargers are just not very good and they are prone to failures.
When I received my second prime, I went out and Purchased a Radio Shack 12 volt wall charger, with a USB adapter that plugs into the transformer prime charging cable. The Radio shack charger is much better for me- no failures and it does not event get warm while charging- the tablet has worked fine for the last 2 months so far without issue.
If you are interested in the radio shack charger, see other posts made by me for specific part numbers. you can order online, or pickup in store at most locations.
Asus needs to do something about these wall chargers. They need to be re-designed so that they do not seperate, and do not require cartridge based adapters- this is a huge problem.
The primes biggest issue with " Prime reliability" is the wall charger IMO- More failures and returned units for this than anything else.
I love my Prime, and the radio shack charger works for me- good luck: and check all of your other options first before returning your tablet... there is a good chance it has to do with the charger itself.
//End- Shutdown of response signal: termination at reply to Android root/ bye.