Hey Jason,
well that sounds good. At least the battery part. For now it also seems like the M92T36 and BQ24193 might actually be ok, too. Might.
If you wait for a minute or two (as long as it would normally take the Switch to boot) and connect Joycons or tap on the screen (to log in), does it make any sound? Try both, since the touch might have broken together with the screen. If you can hear any sound, you probably need to replace the screen. If not, try getting into recovery mode (RCM) if it’s possible with your Switch (check this post to find out more). Try injecting some payload (again, if it is possible with your Switch). Does the screen show anything?
I didn’t really understand the dock part of your post. Do you get any video if you put the Switch into the dock? The Switch’s screen should NOT light up if it properly detects the dock.