On that screen with "tampered" etc (which means it had been unlocked in the past) there would be a "hboot version". Can you tell us what that was - it's relevant if you want S-Off. Also what type of One do you have (GSM, Sprint, Verizon)?
Sorry that was a bit short - was on my phone in a rail station with limited time.
From the description it sounds like your ROM got corrupted somehow. I've never heard of this happening spontaneously, so would be interested to know what you were doing when this occurred - understanding the problem will help with finding a solution.
The word "tampered" did not appear spontaneously. That means that at some point in the past the phone has been unlocked and had the software modified. Did you do this, or did you ask someone else to root it, or did you buy it second-hand? I'm guessing you didn't do it yourself or else you'd have recognised the hboot screen. Again, I'm not being nosy, but trying to understand the state of the phone and how much you know about these operations.
The most important thing though is what you want to do. The word "tampered" only matters if the phone is still under warranty, and you only actually need S-Off to remove that word. So if you don't have (or don't care about) a warranty and just want to get the phone working S-Off is actually not that important. My guess is that to get the phone working again you just need to install a new ROM.
When you try to install "the zip" from recovery, which zip is this? Did you already have a ROM zip on the phone? Otherwise you'll need to download one and push it to the phone (via ADB while in recovery) before you can install it (or use a flash drive and an OTG cable).
The important thing is that ROMs are for specific phone models. There is more than one version of the M7, and some ROMs do not support all versions (hence some of the questions in my first post). So you need to choose one that's right for your phone, then get it onto the device as above. As part of the installation you will need to do a factory reset. As this will erase your apps and data (if those are still intact, which we can't know at the moment) you may want to do a backup first. The custom recovery (CWM) can do a backup of the whole phone - ROM, apps, data. You don't want to restore that backup (would return the phone to its current state), but the paid version of Titanium Backup can extract data from a recovery backup, so if you make a recovery backup (aka a "nandroid") you may be able to extract some of your data from it. If you are confident that your important data are backed-up somewhere already then don't worry about this bit.
Finally, some ROMs work better with some recoveries. So if you have trouble installing your preferred ROM using CWM, TWRP is actually more widely-used on the M7.
Good luck
