id check home button flex that attached to shield, does your old screen work with home button. also back up and fully restore phone. did you use enough heat to pull away the home button? check for any type of damage.
i would swap out the whole d-pad , i couldn’t imagine it being more then a few dollars for the part, the rubber parts are conductive. other wise since its not a flex cable and the d pad is actually on the board. a new board isn’t a bad way to go. if you think its worth it. 3ds are pretty cheap and a huge upgrade
are there any updates that need to be done. also i would try doing a full restore from a stock rom. not a hard reset. you can’t get more pure then reloading your system from scratch. any physical damage to the phone?