Hello!
Since you've already change the battery, and it is still vibrating, it doesn't seem like this is a power issue, or at least not a power issue from the battery/charge port. What I would do first is try to let it charge for a while just to make sure the battery you put in actually has enough of a charge to turn on. I would also double-check to see if you accidentally unplugged the flex cable for the screen or anything else just to be sure.
If those fail, you could try to put the phone into recovery mode and factory reset.
1: Hold the power and Volume+ button, and then
2: When the broken android symbol comes up quickly press the power and volume up at the same time (Don't hold, this might take a few tries)
3: When the menu comes up, choose factory reset (this will erase the phone, so make sure you have your google account login info on hand)
4: The phone will reset, and it should work.
Alternatively, you could try to reflash/update the phone if this does not work. This will require you having a way to put files onto a micro SD card (Either via a slot on a laptop or some sort of external SD card reader/writer). This will also make you lose your data, so keep your google account info on hand.
1: Put SD card into reader
2: Go to https://developers.google.com/android/ot... and scroll down to Oriole for Pixel 6
3: Repeat steps 1-2 from above. In this screen you should see the version of Oriole you're on (ex: Oriole 12)
4: In the link from above, find the firmware that matches what your phone and carrier is on and download it. (You can go to a more recent one if you would like, but you can't go back in versions)
5: Make sure the firmware you downloaded is on the SD card (Don't unzip it) and eject it from the computer (Like you would do with a flash drive)
6: Open the SIM tray on the side of the phone and put the SD card into the SD card slot, and in the recovery menu select "update from SD card"
7: Wait for it to update (I'd keep it on the charger so it doesn't lose power)
8: If all goes well, it should work.
If these both fail, it's possible it could be a board-level issue, or perhaps the battery you bought is bad. It could also be the screen as you suggested, so depending on how valuable the data is on the pixel, I'd try to replace the screen first.
Good luck!
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