I recommend that you download PC Companion to your computer:
http://www.sonymobile.com/global-en/tools/pc-companion/
If you already have it installed you can uninstall it and then restart your computer. Download and install the program again.
In PC Companion > open the option called "file manager" then you should be able to browse you files in your phone.
If the problem still persist you should try to connect to different USB ports on your computer.
If it still doesn't work it would be good to know which Android version you have in your phone and which operating system you have on your computer.
