Either you have not seated the connector for the digitizer correctly or the digitizer is defective on your new screen. Turn it off, open it and disconnect the battery. Reseat the connectors again and test it by plugging in the battery and powering on before assembling everything. If it still does not work...(ALWAYS Disconnect battery before plugging in or unplugging connectors) you most likely have a defective screen assembly.
And as Jim suggested, clean the connectors and look for damage.
Does your old one work? If so, you can try connecting it back up to test with. Also, make sure each screw you remove goes back into the same hole it came out of and do not mix them up. IT MATTERS and can cause damage to the Logic board if you do not.
Post back the results to help others troubleshoot their devices with similar issues.