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If you have a security lock then this needs to be unlocked before a computer will read it - If the screen is fine but the touch is damaged then then you could use a USB OTG cable and mouse to unlock your phone then connect this to a Pc after to perform a backup
Most electronic stores sell them or Amazon or eBay or if you have a female to female USB coupler then your current cable connected to this coupler then to a USB mouse could do the job
You can then control your phones touch function to unlock the phone - However if you have no screen image at all and your security is a pin or pattern lock then I have no help to offer as I'm out of ideas