Unfortunately the situation you're describing could have any number of causes. The easiest way to debug is to hook up an Android device to your pc with a USB cable and open chrome://inspect in a Chrome window. Your device should automatically show up as soon as you start your app. Selecting it will open a browser console. In most cases, you should be seeing an error pop up in the console as you're trying to connect.
Edit: the weinre tutorial above will also net you a debugger, but requires an install and editing your app, where the Chrome console works out of the box. The upside to weinre is that it will also work for non-Android devices.
Edit: Forgot that this will only work if you have debugging enabled on your phone, sorry. Apparently I take that for granted nowadays. Enabling debug mode can be done from the the developer menu of your Android phone. Simply tap the 'about' menu setting seven times in succession and you should be good to go. If you're having trouble there should be lots of tutorials on Google.
If you can't see it on mobile, you might want to file a support request.
One thing I can think of is that you forgot to include a Phonegap package. Not sure, because you also state it works great on your mobile browsers.
EDIT: Dexx his method is correct. You can debug any Phonegap build with chrome://inspect. Looks like I have learned something new today :-). Below instructions might only be useful when you try to debug iPhone etc...
There are ways to do debugging, this requires some manual effort:
That's the way I have debugged a couple of Phonegap builds lately and seems to work pretty good.
If you have debugged it, make sure you remove the script tag again before creating another build / publishing your application. If you forget this (or your phone is not on the same network as your application) you will get a white screen anyway, as it fails to load a dependency