Posting this for continuity, the results.
I actually had an open hot on one leg or branch of the breaker box, that much I knew. Here is how I found out, and what I did.
OK, so I finally got the old lady to rest long enough to unplug all the breakers (physically removed from breaker box). Still had low voltage on one breaker bar. We have a master breaker outside, near the meter.
It's at the top, this was a reference picture I took. Normally has a cover on it.
Ok, so I test the two at the meter... and they're both good there... so the problem is in what I find is called the "service entrance", the wiring from the meter to the breaker box. I should say now, the following repair should NOT be done by someone unfamiliar with general construction principles, and home wiring guidelines. There are laws governing how this type of repair should be done (search "service entrance" for your particular state), and not following these rules and guidelines could result in death, shock, and fines.
So my line runs about four feet underground to the trailer, lift the skirt and the rest is aboveground. According to the guidelines for Indiana, it should be 24in deep, in conduit. It was not. Not 24in deep. Not in conduit. It was 100A cable, run diagonally from ground level to about 18in down where it leaves the meter in sch. 80 PVC. And, just as I expected, I found this:
So, I wasn't sure about which cable to get, so I got 200A cable, thinking, I have at least 100A in breakers just for the outlets. Get cable, enough conduit to completely cover the wire, pulled out the old wire, pushed the new wire through, re-connected on both sides, reconnected all the breakers, and done. We have our hot water, stove, and dryer working again. In addition, the wiring was now up to code, the code violation being the source of the original problem. "Call an electrician" they said, when I can do a better job myself at 10% of the cost. HA! Did-It-mYself!
New wire, not fully connected, in brand new conduit... the lighter, L-shaped conduit under the skirt, going up into the breaker box is visible, that was the only conduit present before the repair. Gaps in the conduit were sealed with FiberFix.
I want to add a few things. 200A cable is NOT easy to work with... it is a little like bending rebar. I used my tubing cutter to strip the insulation... and a hacksaw to trim the ends. Second, this repair is not for the "home handyman", you really need to know what you are doing with electricity and wiring, 240v will travel right up the wooden handle of a shovel. Also, as I said, this is work that is supposed to be done by a licensed electrician or contractor, to "code", so unless you feel competent either fulfilling or violating said code, let someone more competent do such work. Another issue is grounding, if you mess with your service entrance cable, you ABSOLUTELY POSITIVELY need to make sure that the ground at the meter is solid. Faulty ground at your meter means faulty ground in every single outlet in your home, a shock hazard, a fire hazard, and potential death to all your electronics that rely on it.
I hope this helps someone.
Best Answer
If this were my wall: I'd pay the $30 to have an engineer remove the towel rail and fit service valves to the pipework. Then you can take it off, replace it, or what-have-you whenever you want without worrying about the upstairs neighbour. Mention to the plumber that you'll be re-plastering and re-tiling so the service valve is properly proud of the wall.
Then, with the towel rail off, get someone in to plaster it. (Don't try plastering yourself unless you do it for a living, it's much harder than the fellow you'll get in will make it look.)
Then tile away. A smaller tile means you can generally get away with really quite big imperfections, a wall that's a couple of inches off true at the top should be fine. (See here for more on that.)