I have exactly the same issue. It happened yesterday. It was just there, sitting on my desk, one minute it was working and I was checking my e-mail, the next one it was not. The phone now detects no SIM card and if I try to enable wi-fi it just hangs in "enabling" status for some time until it gives up and disables it again. I am not 100% sure, but I think I also had a short time in which wifi was no longer working and the SIM connection still was, I remember seeing the 4G logo and maybe I even browsed the internet for a short while. By the way, I have not replaced my screen. Now I know that I can probably spare myself the hassle of doing a hard reset.
It is really suspicious that this weird problem is happening to several people within a short time frame. It would be cool to hear if HTC has anything to say, but I am also not expecting anything from them now, especially for a phone which is out of warranty.
In case it can help, as the author reported, bluetooth still works and it is possible to connect the phone to the internet using bluetooth tethering on another phone (the good old M8 helped here

). This doesn't solve the issue, but is much better than nothing, most apps will work and it is easier to make a controlled migration to another phone.