A broken Home button flex should not stop the phone from functioning properly, home button functionality notwithstanding.
If your screen assembly is not working, you either have a defective screen or you damaged something else while doing your own repair.
Go back through this guide and double check all the steps. Also be careful to always disconnect the battery before disconnecting the screen otherwise you may damage the backlight circuit.
So I would try these steps:
- Double check that the flex connectors are properly seated
- Visually inspect, preferably with magnification, the condition of the connectors on both the flex cables and the logic board
- Also look to see if any components appear missing or damaged
- Shine a flashlight on the screen to see if you have a very dim image. This would be indicative of a blown backlight circuit.
Hopefully your problem is modular in nature otherwise it may require a micro-soldering repair.