Screen not working after replacement phone on during replacement

Is the original screen still at least partially functional? It would be worth your time to plug the broken display back in and see if it's working normally; that would confirm an issue with the replacement screen.

Being a Pixel owner myself, I've noted a disturbing trend in genuine Google replacement displays. They seem to have a higher percentage of failing right out of the box than I would expect to see from any given manufacturer.

You didn't mention where you bought the display from (or whether it is a genuine Google part), but if you bought it from iFixit it comes with a lifetime warranty. Whatever the case, it seems like it's time to contact the seller about the possibility of a warranty replacement, especially if the original screen is still working.

P.S., Nowadays it's not quite as urgent to make sure the battery is disconnected before plugging or unplugging the display. On older LCD based screens the higher voltage backlight circuits could often blow out fuses or circuits if power was on, but with newer OLED displays it's not as much of an issue. That being said, it is always a good idea to unplug the battery first and plug it back in last, but it's not a death sentence like it used to be.