Worst case scenario: when he jumped on it, the logic board cracked. Solution: get a new device.
Other scenarios
The pins holding the processor heatsink on snapped out, and the processor was overheating. Solution: If it's not already totally fried, reapply thermal compound (preferably Arctic Silver 5) and reinstall the heatsink. If that doesn't fix it, time for a new console.
The connector for HDMI was damaged. Solution: get an HDMI port with solder points, desolder the old one, and solder a new one on. This is highly improbable, though, because HDMI is a digital connection, and the sound wouldn't have passed through.
Sorry to be the bearer of bad news.