My iPhone 5C won't restore! Help!

I was trying to sync my iPhone 5C with iTunes on my computer and it told me I needed to restore my iPhone and put it in recovery mode.So, I did. It started "Extracting software" and it fully completed that step. My iPhone then displayed a screen with an apple and a loading bar. The loading bar would show up for a couple minutes, but would not fill up at all before it would disappear. When that screen would disappear, my iTunes would display this message "The iPhone 'iPhone' could not be restored. An unknown error occurred (4013)." And my iPhone would go back to the recovery. I tried shutting off my phone and unplugging it and tried restoring it again and all of that happened again. I now cannot turn on my phone because every time I try it takes me back to the recovery screen. Now that I have to restore it and it won't work, I'm panicking. I don't know what to do to fix this! My iTunes and my iPhone are both up-to-date. Please please please help me!

Try this -

After you perform each step, try to restore your device.
1. Restart your computer.
2. Disconnect all your USB devices from your computer and connect to another USB port.
3. Use a different USB cable.
4. Uninstall third-party security software.
5. Try restoring using an alternate computer.

If none of the steps are working for you, you might have to kick it out of recovery mode. Get a program like iREB. After you get iREB, do the following steps:
1. Open iREB.
2. Click on Recovery Mode Loop Fixer / SHSH Blobs Grabber
3. Click on Set Auto-Boot True (Fixes 1015 Errors / Recovery Loops).
4. Wait a few seconds for it to do its thing. It will restore the boot-args to the device, save the device's environment, then reboot it. You should then see the Lock screen when it boots up.

If that won't work, go to the Apple Store and explain your situation to them.

Hope I helped!