Not sure but I don't see why you couldn't. It would require you to take it apart though. A alternative would be to purchase a EXTERNAL STOREAGE device, and I highly recommend it. You can buy them pretty cheap and just plugs into the USB port and you can access all your files and etc just the same.
so you have tried a new home button and a new home button flex cable? You may have damaged the home button connector on the logic board, did you try cleaning the connector? Also inspect the connector magnified. Look for any damaged prongs or dirt etc in there...I'm assuming you did unplug your battery before reconnecting the screen and home button flex cables onto the board right ?
Try deleting your message history with the number that you have having trouble sending messages to and have them delete their message history as well and deleting each other out of your contact list and try sending a message again after you've done the steps mentioned.
I've had this happen a few times after a screen replacement. Always do a hard reset first, most the time it will fix this issue. If not the it's the connection of the flex cables to the board itself and or a faulty replacement screen.