Samsung Galaxy S2 black screen
I think your battery is broken or there is another hardware problem. You can do this; try to borrow a similar battery as the one used by your device, use it on your S2 and see if it turns on. If it does turn on then do a backup immediately.  If it doesn’t turn on then try connecting the device to your laptop and see if it is recognized. If it still doesn’t get recognized you better go to an authorized repair center but, there is still no assurance that the data can be recovered.