The camera should still work without the card. If it does not, then there is something wrong with the phone.
While you are at Verizon, have them put in an sdcard to see if they can get the phone to read and recognize an sdcard. Don't give them your sdcard to try...you want to make sure you preserve the pics and music, so don't do anything with that card until you are able to do that.
After you get the sd card adapter, if you are still having problems saving to your pc, there are sdcard recovery programs you can use that will extract your pics for you.