When you first plugged the phone into the computer (assuming windows) it would have installed some drivers to identify the device and allow it to intergrate and work with the PC. The computer should have done this automatically, but occasionally for whatever reason, the drivers may not install correctly. The can most likely be downloaded from Samsung support. When I pull down the notification on the phone, it says "connected as a media device" does yours do the same. When I pull up "Computer" on the pc it has the various drives (C,D, DVD etc) and SCH-I535 which is the phone. When I click on that, I then get "phone" or "card" to choose from, etc.
I'll state the obvious because sometimes its overlooked. Did you try restarting the phone and the computer?
Support - Verizon Wireless Cell Phones SCH-I535 | Samsung Cell Phones
The last thing that I just thought of is the cable, try the stock cable if your not already using it. I have found that some USB cables will charge only and can not transmit data.