The only way to open that phone is through the back. The back will need to be heated up and removed carefully with a pick or pry tool. Sorry this one is not fun

Have you tried a soft reset on that device? Soft reset with hardware keys A soft reset is a simulated battery removal. This is used to power a device off when the screen is frozen or unresponsive and the device it has an internal battery that cannot be removed. It does not cause loss of personal data on the device.   (1) Press and hold the Power and Volume down key for up to 45 seconds. (2) The device will restart and complete the soft reset.

The best way to search is by typing "LCD Assembly SGH561. This screen is a glass and LCD fused screen. Make sure you purchase this one and not glass only. The sames screen works for model number SGH561,SGP511, SGP512 Hope this helps