If the device settings are correct, then the cable could be at fault. I recently helped a user with a different model of phone who was experiencing a similar issue (PC wouldn't recognize when the phone was connected via USB, but charging still worked.) Once he replaced the USB cable, he was once again able to reconnect. The newest myTouchy device has only been out a few weeks, and as long as there were no physical damage you should be able to exchange the charger and cable if it is found to be faulty.
It is also possible that the settings may have been changed. I found the below information in the User Manual available here: http://support.t-mobile.com/docs/DOC-2794
Transferring music files using USB mass storage devices
1. Connect the LG-E739 to a PC using a USB cable.
2. If you haven't installed the LG Android Platform Driver on your PC, you need to change the settings manually. On the Home screen, touch the Applications tab > Settings > Storage, then select Mass storage only.
3. Touch Turn on USB storage.
4. You can view the mass storage content on your PC and transfer the files.
NOTE: You need to install a microSD card first. Without a microSD card, you cannot use USB mass storage.
NOTE: If you installed LG Android Platform Driver, you will immediately see the USB Mass Storage screen.
Hope this helps!