"Can I upgrade the processor with the 2.4 mid 2010 model?"に関する回答It’s definitely an easy job to replace an A1342’s 2.26 logic board with an A1342’s 2.4 logic board. No other component needs to be swapped or modified. I’ve done this upgrade to many “late-2009” A1342’s with damaged logic boards.
"Faulty home button, doesn't work"に関する回答Error 53 is a vestige of history. It is no longer a problem since Apple released iOS 9.2.1. As long as you're not running iOS version 9.2.0, you shouldn't see error 53. See https://techcrunch.com/2016/02/18/apple-apologizes-and-updates-ios-to-restore-iphones-disabled-by-error-53/
"Screen only works when phone is open"に関する回答My first guess is that a cable on your new display is unreliable: As the cable flexes when you close up your iPhone, one or more conductors in the cable are losing their connection. (1) If evidence shows that there is an iffy conductor, I'd remove and reattach the display, in hope that it's simply a poorly seated connector. (2) To determine if it the simple case that the display is simply not displaying anything, I'd try using a USB cable and see if the device shows up in iTunes even with a non-functional display. (3) If the old working-but-cracked display is still available and viable, I would temporarily re-install it and see if the old screen's behavior is normal.