Phone won't turn on after professional screen replacement

Hi-

Today I got my iPhone 5s's screen replaced at a local irepair shop. The store had 4.9 stars and all reviews were positive, so I figured it was a good choice. I dropped my phone a couple days ago when I didn't have my case on, nothing major, just a few cracks in the screen, but I wanted to get it fixed. For the first couple of days before I got the screen repaired there was a small discolored spot on the screen that tinted the area yellow, but it went away after I took off my Lifeproof case, so I figured that the pressure on the cracked area by the case was causing the effect, and didn't think much of it.

However, today after I got the screen replaced everything worked fine: the screen wasn't cracked and I went straight home and put my Lifeproof case on to prevent accidents. I barely touched my phone on the way home, so there was no way I could have dropped it or caused damage, but a little bit after I put the case on I noticed a small crack in the upper left corner. I don't know if the repair people may have put the new screen on crooked/not tight enough, but I'm positive that the crack appeared after I put the case on and not after being dropped or anything. About an hour after I noticed the crack, I was typing a message and the screen started glitching, clicking random letters, etc. I figured that it was an aftereffect of the replacement so I tried to restart my phone by holding the power button and home button, but after it turned off it wouldn't turn back on. I plugged my phone into two different computers and iTunes recognized the phone, so I'm thinking that it might just be the screen that's broken. Any ideas on what to do?