Why is it not turning on?

The lid has a function telling the logic board the lid is either open or closed! When you remove it you remove the input. If you look on the backside of the logic board you can see the two Hall Effect sensors MacBook Pro 13" Retina (2019) 2.4 GHz Logic Board with Paired Touch ID Sensor look at the left and right sides the little bump outs with a device that is standing proud is the sensor.

So in order for the displays signal to travel to the external the lid needs to be left on the system with the lid closed. Then using USB wired keyboard and mouse/trackpad you can use your system. If you can still gain access you might still be able to setup a Bluetooth keyboard and mouse/trackpad.

As far as that little cable that is the battery monitoring data cable which also needs to be present for the system to work properly. If you damaged the cable and/or the connectors that may require a new cable and if the connectors are damaged deeper skills to replace.