If you still have your old screen, installing it on your iPhone together with the front cam flex. Home button doesn’t have to be transfered for the phone to function. If it does work, you’ll know that the problem was the missing film. If not, your front camera flex might’ve been damaged while removing it. The sensor is not attached very tightly so it can break off of the cable quite easily.
Check if it’s bent. If it is, your motherboard might be damaged. This isn’t something that you can fix yourself. If it is not bent though, check for water damage. The iPhone 6 and 6+ are not sealed, so they are not waterproof.
Sounds like a hardware problem. I think it’s water damage. I would not advice repairing the device yourself. Whether the water has only damaged the camera or more is impossible to tell without opening the phone, and if more has been damaged it could be unrepairable. I would advice making a full backup of your phone and see if a repair shop nearby is willing to repair it, whether it is by going there yourself or sending them an email. Always be careful when repairing water damage, as it can always cause more problems than what you can see.