We primarily focus on parts and repairs for iPods, iPads, iPhones, and Zune Players. We also offer service and parts on Kindle Fire , Kindle Fire HD, Galaxy Note, and other smaller consumer electronics.
I have seen this issue once before, and it turned out to be related to the dock (unit thought it was plugged into a docking station/external rig, so it put all of the audio out to the dock and not the speakers). Try using compressed air to clean out the dock and the headphone jack. If larger or more stubborn debris won't budge, use an exacto blade to carefully knock it out.
You may want to check the miscellanious chips located around the sides of the connector for the LCD/Digitizer assembly. There is a chance that you could have damaged one while lifting up the connector from the old display.
There could be damage/corrosion on the home button circuit or on the dock (The home plugs into the dock module, which plugs into the circuit board). If you are comfortable and have the tools, you can open up the phone and have a look at the dock to see if you see nay corrosion. Examining the home button circuit will be a little trickier, as you have to completely take the phone apart to see the entire home button circuit. If you do see any corrosion, you can attempt to clean it using a brush (like an old tooth brush) and Isopropyl Alcohol. If you are not so comfortable with taking it apart, there are several repair company's out there that specialize in iPhone repairs and would be able to help you. They are just one Google search away.