IPhone 5 Went to a Blue Screen and Won't Turn Back On?

I currently own an iPhone 5 and last night I went onto Instagram and it immediately went to a blue screen for about 2 minutes and then completely turned off.

No matter what methods I use (holding home/power button at same time, volume buttons, unplugging usb and from dock and then into computer), nothing works.

I left to charge overnight and tried to turn it back on this morning but to no avail.

I know the phone had about 60% battery left before it went to a blue screen so I know that it's not because of low battery.

There's no response whatsoever when I connect it to my computer.

Any suggestions? Tips? Answers?

(I have an appointment with the apple store on Tuesday but I'd really appreciate it if someone could help me out now since I kind of need it soon).

Thank you.

Added (1). @ShortyG I don't have the kit to remove the battery on the iPhone 5. You need special screwdrivers for it. Should I just order the kit online or wait until the appointment for them to do it? I'm afraid that if I go to the Apple Store to do it, they'll charge me more money.

Try removing the battery, put it back in after about a minute. This will work on some phones, some it won't. I don't know about the iPhone.