It's possibly one of the main earth cables packing in. The one going to the gearbox is known to corrode internally. It can look fine from the outside, but the copper strands at one end corrode through one by one where they go into the crimped terminal until there aren't enough left to cope with the heaviest demand, which is the starter motor. So other electrics can work fine, but the starter won't turn over.
The easiest way to see if it is this the fault is to use a stout jump lead to temporarily join the battery negative terminal and some solid part of the engine block or gearbox. There are several bolt heads as suitable candidates. Don't clip on to any of the less-solid metal pipes though. If the engine starts with the jump lead in place, you know it's the earth cable that's shot. There are two fat ones - between battery and body, and battery and gearbox. The latter one is tucked away under the battery tray.
This problem doesn't normally make itself felt until the colder weather (when the starter motor has to work at its hardest) so in this case I have some doubts, but it's worth a quick try.
