i had the same problem, only in my 9305 was bigger. Stock rom , black wallpapper, all syngs off, drain battery was down very fast. I make a test and put the phone in airplane mode. I checked that wifi, b/t, radio was off and from 12 o'clock night until 7 o'clock morning the phone from 59% went to 16% . Durining the day , i use only GSM, WIFI and B/t on, the use of my phone was 8-10 phone calls, little internet and from 7 o'clock morning with 100% i had to recharge it about in 16.00 o' clock. I tried curstom roms but nothing solved my problem . Then i switch it to orizinal rom and went it to servis.Now i am w8ing to return my phone from servis and i will write what they told me.
PS : My phone is in servis for 8 days now