I am thinking it's more likely needing a new dvd drive.
I also had a issue similar to this when doing a recent update myself would have been the update prior to the one you've had the issue with it started the update then just came up with the error update failed please try again. Problem was that it didn't take us back to the dashboard it just sat there with no choice other than to power off the console, which upon restart would go straight back to the same error.
I ended up with a near identical conversation with MS about where to from here and they were apologetic and advised sending in for a repair also. In the end I took it to someone I knew who mods consoles got the latest mod done and got the console fully working again with no issues since. All up cost just under $100.
Either way I hope it all works out for you in the end and that you get your issue resolved without having to spend much more $$$. :-)