Iphone 5 not working properly

Hi, Recently my iphone 5 has been acting up a lot. first it started to lag a lot, then battery icon will tell me it's fully charged, but it's not. Now the screen will turn green (sometimes it will have lines appear) turn off and turn back on. not sure, but Before this, there was a storm and the electricity left and came back very fast multiply times. It has suffered a few big drops with a otter box on, and was left charging in a car that was turned off ( Not sure if that would effect it ). I have backed it up and restored it and it is still doing this. I have apple care and what not so replacing it isn't a big deal, but I just want to know what I can do. Thanks.