thetypewriterman wrote:

Obviously I cannot see your machine, but it sounds as if there is a problem with the line-lock mechanism, possibly a return spring missing or detached.  When the machine is in the normal position, it 'thinks' that it has reached the right margin, and locks the keyboard.  With the machine tilted back, gravity takes the place of the spring and the keyboard releases, albeit temporarily.  You might be able to test this theory by trying the margin release button to see if it has any effect.  If you put your fingers under the machine, you might well have knocked a spring off without realising it.

Ah. Much food here! I had already had the experience of knocking out springs by handling, so I did think of it here, and may be the case though I have not found the spring yet. I did find a spring hanging from a lever to the far left near the front (from the top) attached to a lever which has something to do with shift and shift lock. This does not seem to be connected with this issue - or any issue yet that I have been able to find - and I cannot find a corresponding hole to reconnect the other end.

The margin release is a small tab in a nest of levers on the left side of the carriage which merely raises the bar on which the margin stops sit, and allows the margin stop to clear a post. A second post descending from the margin stop seems intended to move a lever but misses it - I have not tried to correct this, but moving this lever around does not seem connected with the issue. This lever has working spring loading. Moving the margin release does not unlock the keys, but the interesting thing is that while typing in the gravity assisted position, the keys do not lock at the margin! They just keep typing on top of the last position. So something would seem to be amiss here, and I think you have hit it. Something is moving around by gravity which locks and unlocks the keys, which should be locking by some interaction with the margin. In a very quiet room, if I gently raise the machine listening with safe cracker intensity I can hear a very faint click when the keys unlock and the hidden whatzit shifts. 

With all the clues I must be a dull boy if I cannot eventually find the offending mechanism.

The machine seems EXTREMELY sensitive to the surface it is placed on - since it was designed to be screwed down to a flat wooden base - and even rotating it on a very slightly lumpy surface affects some functions. So if I do get it working properly without the case I should perhaps find an attrractive piece of wood to screw it down, or at least raise it on feet.
 

Okey, Dokey. It's working again - for now.

I fear I have exhausted the Patience of the Board, so I will report the sophisticated method by which I restored function another day!