You didn't say but my guess is that you want to recover some data.
R1. Starting with it off, press and hold the volume up and the home button, then press the power button until the short vibration. Wait about five more seconds then release the other two buttons.
R2. It should now be in Recovery mode. Try ADB.
D1. If no access through ADB then do paragraph R1 again but instead of volume up, press volume down.
D2. After releasing all buttons in D1, press and release volume up.
D3. It should now be in Download mode. Try ADB.