If your AMOLED screen doesn’t show any picture but the phone seems to be working fine otherwise, you will definitely need a [product|IF347-002|replacement screen].
For the mean time, you can drain the battery and stop all alarms by putting the phone in “Download Mode”. This can be done by pressing VOL DOWN, POWER, and HOME together for 15 seconds. You won’t see any feedback on the screen, but the phone should stay in this mode until the battery runs out.