I had this same issue for quite some time on my S3. After talking with Verizon several times, I realized that they had no clue what was causing this. I factory reset my phone a few times and the media server process didn't show up until I put my music back on the phone (internal storage, not SD card). Then, it was only a matter of time before it was back up to using 60% - 70% of my battery, even if I did not listen to the music on the phone. On a side note, my music is in .wma, .mp3, and .m4a format. When I moved the music to the phone's storage, I was asked if I wanted to convert it and I said no. Every time, the media server process would creep up and kill my battery. Two days ago, I did another factory reset and when I moved the music to the phone, I chose yes when asked if I wanted to convert it. I noticed that it only converted the .m4a files I had (converted them to .wma). Since doing that, I have not seen the issue with the media server process. When it is on the list, it is at the bottom and uses no more than 3% - 4% of the battery and eventually drops off. I'm not sure if this will fix the problem for everyone, but it is worth a try if you have .m4a files on your phone. You may want to factory reset your phone first, then move the music back onto the phone, converting it in the process. I hope this helps.