This sounds like what I am getting in my plane setup. Since new firmware update my ESC does not see any PWM signal and therefore beeps every 2 seconds and I have no throttle control. The blue LED on the Ardupilot board flashes very fast which I believe indicated a bad servo signal. I have since ordered a new Ardupilot board from Sparkfun, thinking I have a bad MUX chip on my old version 1.0 board. And yes when I calibrate the radio I have readings of all my channels in the GCS software.
On APM2.0, because you must hit the reset after powering via BEC, it often is the wrong timing with the ESCs trying to go into their programming mode and they don't accept any input. So yes, I have seen this before and what it takes is 3 or 4 tries of disconnecting a reconnecting the battery and pressing reset to get everything "in sync".
The solution is dificult but EXTREMELY effective, flash the ESCs with a hacked firmware which eliminates all of the problems because then the ESCs no longer go into program mode, nor do they require calibration and they are more responsive. Again, it's dificult because you must cut a hole in the heatshrink to access the programming pads, either solder or make a pressure contact system connected to the AVR programmer, and then flash each one, but once it's done-never have a problem again.
I had the same problem with the new APM2.
Just try to change or reverse the remote inputs until it works.