The phone will boot and charge without the screen. However, if it is locked with a passcode, you will not be able to access the data from the computer. If you don’t have a passcode and the computer is already “Trusted”, then you would have access to the data.
If the phone doesn’t boot or charge, then you have a logic board issue. If the data is important to you, then a repair shop that does micro-soldering repairs may be able to recover the data for you. You could then either have them replace the screen or turn into into your corporate IT group to have replaced.