Hi,
Great that you’re having an interest in having a crack at repairing and learning about your phone.
First thing I would do is disconnect the battery and do a voltage check on the battery.
Next I would do a voltage check on the output of the onboard battery connector.
If you have voltage output on the connector then your charging port is working.
If the battery has low or no voltage it may be unable to take or hold enough charge to power the the phone.
You can try to put it on charge for an hour and then see if you can get to the recovery screen with the button combinations (volume up & power) until you see the android logo then release.
If you’re not sure about this, there’s heaps of videos on YouTube to check, just search for Pixel 4 won’t boot or Pixel 4 dead no boot.
If you make it to the recovery screen you can try selecting “wipe cache” an see if it restarts with a display.
I’ve found that Androids are fairly hardy as far as the mainboards go unless they’ve been water damaged.
One area to consider is the flex cables from the port to the mainboard.
Most of the above is only going to cost you some valuable learning time.
If you’re lucky, the $ value may only cost you the price of a battery.
Keep an eye (or ear) out for any signs of life as your display may be dead.
If you find that there is some vibration but no screen you can attach it HDMI on your TV to see if it is actually on.
Hope this helps