IPhone froze now won't turn on?

I have and iPhone 4. I shattered the screen last week so had it replaced today at a shop. It rebooted and froze so they did a factory reset. Worked fine until we got home and restored from a backup. As it was completing the restore we got the white screen. I reset using the middle button and lock button and managed to get a broken dark grey screen with slight white edge. After a few more resets I finally got to the lock screen. However this screen was flickering and I couldn't do anything. It turned itself off after about a min. Three tries later and now it won't do anything at all. Can't reset, can't charge, won't respond when plugged in to the laptop. Help!

Added (1). Will be going back to the shop but as its the weekend it is closed.

Added (2). Will be going back to the shop but as its the weekend it is closed.

Added (3). Don't have tools to open it

Added (4). Don't have tools to open it

Added (5). Unable to entre DFU mode as laptop won't even respond when USB cord plugged in and phone won't respond to buttons being pushed.

Take to the shop again

Try removing battery for a sec my Samsung did same thing tonight. Working fine now.

Obviously they screwed something up replacing the screen. You need to take it back. This is why I would always have it fixed at the apple store (unless there isn't one enar you).

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