Worth trying to fix?

Trying to determine if it is going to be worth trying to fix my 5c myself or not.

Several things happened and now all my phone does is make a pong noise when it's plugged in. I got this point after the battery started over heating after being on for certain amounts of time, then after a while the LCD would fade and get vertical lines down the screen while fading out entirely. The final thing is that I accidentally dropped it, and now it doesn't turn on at all and just makes the noise described above when plugged in.

I'm thinking if I replace the LCD and battery I will be okay, but I don't want to invest if its not going to work. Please help! TIA