Some phones won't work without a SIM in them. If that is the case here, you would need to put a SIM in it. Even if it is a non-working SIM, it will usually allow the phone to turn on.
The only thing is to try to connect to it via a usb cable to a PC and hope it connects automatically ... without the screen to tap (middle left to enable usb) this is going to be hard.
Some phones won't work without a SIM in them. If that is the case here, you would need to put a SIM in it. Even if it is a non-working SIM, it will usually allow the phone to turn on.