Why does my iPhone 4 only work when charging?

I dropped my iPhone 4 on my way into work today and when I went back to check the time a while later, it was off and wouldnt cut back on. When I was leaving work it cut on for about 30 seconds then cut off but now it I ky turns on and works when it's on the charger? Does this sound like a simple fix? I kinda don't think it's because I dropped it because I been having issues with this phone since I got it and earlier it was really low when I would call ppl. And also while I'm charging it right now the percentage isn't going up. I could've sworn I just seen it go down. Please help. If its fixable

Does your phone have insurance? If so, go to check it out.
I've never actually had an iphone or have enough experience to see if the back cover can be flipped out (i know, where have I been in the electronic industry haha) but if it does, just open it and check around to see if it has a water damage, most phones have an indicator in the back which goes bright red when your phone has been in contact with water which I doubt it does from your dilemma. Also, it could be the battery so maybe you can get it replaced?