Well you can rule out the non "essential" components, the camera, the vibrator, the antenna, the volume buttons etc. pretty much anything the phone turn on without. The LCD display is working since the apple icon comes on. The battery works since you tested it. It attempts to turn on so its most likely not the docking port. The only place I could think a problem with the logic board. It might be the part at which the battery connects to the logic board, since it is unable to turn on.
Maybe try some elbow grease or some kind of that remover since I doubt that a tea kettle is made to allow its bottom to be replaced and it is most likely fused to the body of the tea kettle unless our talking about its base then that as far as I know is replaceable. See if its bonded to it or not, that's the best way to find out. If its bonded with glue or any other method, that isn't a fuse or weld or any other permanent bond, then its replaceable.The hard part iis finding the part. I would try Google shopping.
Well by suddenly disconnecting the power, you could have done damage to the software of the iPhone. You should always turn it off to prevent damage and data loss. I would think you may have to replace the battery. Also check to see if anything looks different ie there is an area that has turned black . If thereis gently clean it using isoproyl alcohol not the kind that you have in a medicine cabinet, that has to go low a concentration. Get some with the highest concebtratiom you can get. Then clean the area where u see damage and if that does work the part may need to be replaced.
It may need a new antenna. Check to make sure all of the connections inside are good and for any damage. If any connections are loose tight them and then put the phone back together and try again. If you are still getting good signal it is probably just the WiFi portion.
Yeah I had that problem too. You need a new battery. Replace the battery using the guides on this website and that problem will be fixed. However, there might be more problems with the device so be prepared