For those interested, I have resolved both problems by replacing the battery.
The battery was reading as having only 1.2V. It is less than two years old. My alternator was tested recently too, and is fine.
I'm a bit confused about all this:
- the garage tells me that their automatic diagnostics test the battery level. therefore it was fine (and charging) two weeks ago (hmm... unlikely)
- the garage tells me that there is no link (in terms of functional degradation) between power and gearbox. This does not add up to me. I'm sure the ECU/gearbox controller uses CMOS components which are voltage tolerant but i guess they measure speed through the use of strain gauges and equivalents. these rely on clean and steady voltage within CMOS tolerances. So if the battery voltage is dipping or below/marginal to lower CMOS thresholds, the strain gauges/speed sensors will be generating bogus data.
- the garage tells me that (although they did test) validating the battery is not part of the diagnostics for a faulty gearbox. this means that had they gone ahead and changed the gearbox (3.3k+labour), it would (i) not have had a positive effect and (ii) would not have been necessary and (iii) i would have no comeback - i'd have to pay even though it, to my mind, was clearly negligent.
- I also think that there is still something suspect with the wiring loom. a fully dead battery in less than two years is unusual in my experience. i do 100km runs, not shopping trolley visits.
if anyone has any comments or advice i'd be really grateful to hear from them.