No connection after power surge

Hello ASBO 55 NORM

First off, sorry to hear about the lightning strike. Secondly, It may be the actual HDMI port inside the Xbox has been damaged as most hardware components are very delicate and can even be damaged from a small static shock.

In regards to your saves, it should all be on the cloud, due to the sudden shut down of your Xbox when your strike hit, chances are anything you done during that session may not have saved to the cloud but apart from that with a new xbox you should be able
to access your data.

That's bad, A lot of electric devices can be broken or later gives trouble.

Are you sure that the TV works fine (tested with another device through HDMI?)

If a power cycle doesn't work as suggested by Tarnend, there's not much else to do unless you haven't tested multiple TVs yet. I work in IT and have seen power surges kill a lot the devices I work with.

As far as game data goes, your game saves are in the cloud as long as your console has been connected to the internet since the last time you played. If they replace the console instead of repair, your saves will sync to the new one the next time you launch
a game.

if you unplug the power from the xbox then plug it back in then press and hold the power button on the xbox for about 30 seconds, does the display come on if its using its basic display mode?

It sounds like its blown the graphics chip if it doesnt come on still and also i would have thought that any repair would actually be a replacement tbh as it wouldnt be a cheap fix i cant bet unfortunately

Just as an after thought, do you use a power surge protector at all? If so try connecting the consoles power supply directly to the mains power outlet bypassing the surge protector.