Can a cracked screen damage the phone

I posted something similar to the pixel subreddit a bit ago but haven’t seen a response.

I bought a replacement battery off Amazon a few months back since my Pixel 2 was exhibiting the same "dying battery" symptoms as my Nexus 5 did years ago. I was very hesitant to do the replacement myself for fear of breaking the screen. I've done lots of iPhone screen/battery replacements as well as replacing my N5 battery and screen several times all without issue. I was not concerned about the process, just about dealing with a glued down screen.

Of course, my fears were justified. Not only did I use too much heat on one corner of the screen and turned it white, I was too aggressive near the bottom and ended up cracking the screen.

I continued the battery replacement and re-attached the cracked/burned screen to see what would display. I got a few flashes of light but really nothing else. As I powered it on I could feel the vibration motor confirm power on.

I decided to put everything back together except for the screen. I left it detached and put the phone on the charger. Two days later, my new screen from Amazon arrived and I connected it. Got no response from the screen but again felt the vibration motor do its thing. The screen was completely dark.

Now I just got another replacement screen from Amazon on the assumption the original was bad. Before I attempt this again, is there anything that I could've done during the battery replacement that could have damaged the phone in some other way? I'd think the fact that the phone vibrates after powering it on indicates the phone should work. Could the screen connector be damaged / shorted somehow? I've looked at the connector with my magnifying headset but don't see anything wrong and the battery replacement went smoothly following the iFixit guide.

Does anyone have any ideas before I potentially destroy another screen? Does powering the phone on without a screen damage the phone? Can I power on the phone without the screen attached and try to see it from a computer? Can I disconnect the battery and power up the phone only on the charger (to eliminate a wonky battery)? Any other things to attempt? Are there schematics floating around anywhere? I'm not against probing around with a multi-meter if necessary.