Angels have the Phone Box
Yeah, I'm sorry. I just can't imagine what happened to cripple the system so severely - it just doesn't make sense to me.
If I remember correctly, that was Office 2013. Starting with 2013, you have to go online, sign into your MS account and download the installer to get it on your system. Your Office key is then registered/linked to your account, so even if you don't have it anymore, you can still get it, and reinstall. I'll have to look up the site address and instructions for you, but I know that's how it works - I've done it myself for a couple people. Let's do that before you start the clean install, just to make sure we have everything we need.
Generally, hash mismatches are nothing to worry about, and I always ignore them. If we could have just gotten the setup.exe to run from the v1607 ISO, everything would be fine. I can't understand why you get an error that Setup Cannot Start. I have never had that happen, in all the repair installs I have done, or had someone do. It just doesn't make sense to me. You should be able to mount the ISO, (in your case, CyberLink Virtual Drive), use File Explorer to navigate to setup.exe on the virtual drive and double-click it, and it should run! Simple as that. I just can't think what would prevent it from running (other than infection, which we've ruled out).
I'll go find the Office info and post it before I sign off for the night.