MacBook Pro early 2015 not turning on and not charging
Your MacBook is dead.

Without putting hands on, I would guess that you have an issue with the DC-in board.  It's the interface between your charger and the logic board and battery.



You have already done the requisite diagnostics:


Verified the your charger works
Verified that known working charger doesn't work on your MBP
Attempted to boot with battery disconnected


One final test you could attempt (if you have it available to you) is to use a battery from a known good MacBook Pro of the same model.  If it boots, you will verify that the logic board is functional and confirm it's the DC-in board.

As far as the trackpad goes, it has no relevance here.  It's ultimately a USB device and if the MBP has no power, the trackpad won't either.

If it is the DC in board, it's a relatively easy and inexpensive fix.  iFixit.com has excellent instructions.  It is still possible that it could be a logic board failure, but based on my experience that's it's unlikely.