Often times, a reset will solve the problem. I have changed dozens of digitizers and lcd's in iPads and have simply gotten into the habit of doing a soft reset every time. Try that and I am almost positive it will solve the issue.
Best way to solve this problem is to put the phone in a Ziplock Freezer bag with some of the little silica packs that you find in shoes, backpacks, purses, etc. Get as many as you can and leave the phone in there as long as you possibly can. I would recommend at least 2 days. That should fix the problem.
I have seen this before and it is a damaged proximity sensor. All you need to do is change it out and restart and it should be fine. The proximity sensor is the flex cable that contains the selfie camera, proximity sensor and ambient light sensor. Should be a very cheap and simple fix.
With water damage of any kind there is a possibility of strange and unforeseen damage. I would start by double checking the battery. I have a MB Pro that the battery started going bad on and started swelling and it directly effected my trackpad. If that isn't the issue I would replace the trackpad and the little microswitch that it is connected to. If that doesn't work, you probably have some other damage from the water to the motherboard.
Are you meaning that you folded the battery when you tried to repair the lcd? If so, you will probably need to replace the battery. They are pretty durable as long as they aren't tampered with too much. One thing you can try is to do a hard reset(home and power button for about 30-45 seconds) and see if that makes the device come on. If that doesn't, you will need to start systematically checking for power and video troubles. I would start with that battery...
Gently pry up on the end of the battery closest to the charging port, use a small pair of tweezers and grab the loose end of the strip and gently pull on it. I find that spinning the tweezers to coil the strip up on the tweezers helps a little bit. Take your time and pull gently and they will typically come out easily, but don't feel bad, I have broken several hundred of them and they always come out with a little patience.
What cover are you talking about missing? Sounds to me like you got a damaged battery or your charging port is not allowing the proper voltage to get to the battery. Typically, a boot loop on an iPhone is caused by a battery issue.
From my experience the colors are the phones way of telling you that something isn't right with a part that is installed. Typically, it is something like the proximity sensor going bad and needing to be replaced. IF the phone was recently worked on, I would take it back to whoever did the work and have them double check their work. If you did the repair, I would make sure that you didn't inadvertently damage a part while doing the repair.