My understanding of the 4310g ver 5.4 is that the web browser is embedded in a flash pane. Consequently, there is limited functionality on any web page with the exception of three HTML 5 tags, these being audio, video, and canvas.
As such, it would make sense that any external website that you request via the 4310 would not have basic interactive capabilities that you'd get with a regular computer. I'd suggest trying to set up a basic HTML page using the canvas tag to see if you can achieve touch interactivity.
Flash is handled differently by the DMP, so I'm not suprised to hear that flash works without a problem.
Just my thoughts.
Good luck.
-Michael