did you disconnect the battery when connecting the new screen? A lot of iPad faults are caused by connecting accessories (the screen is one of them) at 12-16V. This is usually tragic. In the right hands (first rule of electronics: do not work on live current unless you are doing a test. Otherwise: never, never) sometimes it works. Only sometimes.
When connecting the screen - people try to plug the connector into the port, sometimes they wander ... moving a little left, a little right. Some use force ... believing it didn't pop in ... It kills iPads like yours. By moving the connector over the pins, you find those with signal voltage (0.3-1.2V) and sometimes those with power supply (3.8-16V). Imagine what could happen to the delicate electronics destined for 0.8V when you serve them 12, 14 or more volts.
How to fix it now ... it would be nice to check your new screen is still working fine. Connect it to another tablet (if you have the option, if not - ask a technician at a good repair shop) and test it. If it's ok, I can use it again.
Disconnect the battery as first thoing. If you have an idea of electronics, you can handle it. I will assist remotely :-) You will need a meter - check and write down the resistance of all pins in the video port (long vertical strip, two horizontal strips are touch ports). You will need to solder something, so a good soldering iron is required. If you don't feel up to it, find a good electronics - he will know what to do.
- regards and fingers crossing :-)