I notice that your jQM file is called
jquery.mobile.custom.js
Was this created by
the download builder? Modified by hand? Something else?
Did you try with
unmodified, standard jQuery Mobile?
I also see you are
using jQuery UI Touch Punch. Not sure why you are using
this, since jQuery Mobile already supports touch events. Even
better, it merges touch and mouse events if you use the
"v" callbacks. (e.g. vmousedown , etc.) I doubt that this
plugin is meant to work with jQuery Moblle, Does the documentation
state that it is? Did you check with the author?
jQuery UI and jQuery
Mobile are NOT compatible, and you CANNOT interchangeably
use their plugins. A few plugins "work", some others
can be used with some workarounds or modifications, and a very
rare few third-party plugins are actually designed to work with
either. ( jquery.ui.map is an example of the latter.)
jQuery Foundation has
a plan to make jQuery UI and jQuery Mobile compatible with each
other. That's a couple years from completion, I believe.
Even so, that won't magically make third-party plugins work
until/unless the authors update them.
I didn't look at
shimmy_min.js (where I
found touch punch) further to see if there are potentially
other incompatible plugins in that file.