I think I had a similar problem (minus the beeping) with my last build.
It turned out that I had forgotten to power the ESCs , just as seems to be the case for you.
The issue is that the servorail does not provide power itself from within the pixhawk.
There are two options:
1) Power the servo rail via one of the aux ports
2) Create some kind of mini power distribution board for +5V, power that from your BEC and then plug the red and black wire from your ESC into there (keep the white cable plugged into the pixhawk of course for signal).
Option 1) is very simple
Option 2) is some work, but has the advantage that you have less cables connected to your pixhawk, which potentially reduces to vibrations that are transferred (via the cables) to your pixhawk.
Just thinking - an even simpler issue could be that you have plugged in the ESCs cables "upside down" maybe?
Hope this helps, good luck
P.S: A pic might help...