Is there a way to fix E1xx errors?

Well, that is quite unfortunate.... it may just have bitten the dust.

Have you left it powered off for a few hours then tried again? Literally unplug all cables from it and the wall, let it sit for a few hours, then plug it all back in and try to power up?

I take it you've tried a factory reset as well?
https://support.xbox.com/en-US/xbox-one/console/reset-console-to-factory-defaults

Hi FRAGaholic UK,

Thanks for the reply! I noticed that you've tried pretty much all the troubleshooting available to resolve an E-type error, including the OSU option but are still having difficulty in getting this resolved.

One other thing to consider is if your profile or console are enrolled in our Preview Program for Xbox Insiders, the troubleshooting may not work as intended. If you are an Xbox Insider, we recommend reaching out on the
Xbox Insiders Reddit pagefor further help.

You can also report this problem using the Xbox Insider Hub app on your console or from PC (even if not an Xbox Insider) so we can investigate it further:

1. On your console, install the Xbox Insider Hubapp (if you don’t already have it).
   
2. Hold down the Xboxbutton on the controller.
   
3. On the power menu, select Report a problem.
   
4. Describe the problem in detail, including when it happened, if you saw any specific error codes or messages, and if you were using any specific games, software, hardware, or accessories when you encountered the problem.
   

Should you (your console) not be registered in the Preview Program for updates, and as you're experiencing difficulty in setting up a repair online, I would further recommend
contacting Xbox Support by requesting a call back directly so that they may do so on your behalf.

I hope that this information helps you out a bit more! Let us know.

Hmm what's the actual E1xx error?

Bump.

I take it from the lack of response that my only real option is to buy a new console?