Welcome to Android Central! Are you using the original USB cable? 3rd party cables don't always work well.
When you connect the phone, are you also unlocking it out of the lockscreen? If the phone is still on the lockscreen, the computer won't have access.
If you want to transfer music and have a microSD card, it's probably easier to take the card out of the phone and insert it into your computer using a fullsize SD card adapter. Then copy your music over to the Music folder on the card. When you reinsert the card back into your phone, it should detect the new music.