OK, I contacted support about my Putty issue and found that I have to load the key every time I use it...ok, now that I know that, no problem.
So I got that working again.
But I was so tired from beating my head against a wall over this for about 3 days straight of doing nothing but Moodle, that I've yet to get back to this.
I have one other thing I'm working on for something else that I need to get set up pronto so I can start taking orders on it...then I'm coming back to this Moodle issue, which I still haven't solved.
I did try to go back to my old install (I paid for another month at old host so I still have access, and pointed the nameservers back over there again) and for some reason THAT is broken now....no idea... 404 error there. I just gave up on that, I don't have time to troubleshoot something new. When I left it, it worked just fine and I've not touched it since.
Now I'm back to thinking I'll just do a fresh install of Moodle on the new host (instead of copying old Moodle install) and get that working first...and then copy the old moodledata folder and import the old database into the new? But I'm trying to figure out the best order to do this, if it's even possible... I haven't completely understood how this works... so if anyone can tell me if this is even possible, or if there's a way to make it possible, I'd love to hear it!
Since I'm not sure what's breaking my install, I'm really just trying things out to see what will work...