Problem solved and a useful tip!
Thanks Nomad - problem sorted, Garmin emailed to say it was a reset job, which we had tried - BUT the important point here is that the unit can only be 'reset' when it's turned off. We had only tried to reset it when it was switched on. Anyway, in case anyone has the same problem, press OK + page button + on button together while the unit is switched off, and it will come on with the question 'are you sure you want to reset the unit' to which the answer was yes! It reverts to displaying the USA, but upon acquiring satellites it will display Europe again (although obviously without regional mapping which must be reinstalled via MapSource).
It is important to know that Quest units can only store a maximum of 254 Route Via Points, and once you exceed this it will delete via points already on there. This is a complete pain and best avoided by ensuring that before you download maps and routes your Quest is clear of any pre-existing routes and via points by deleting any saved routes, and that you have not exceeded 254 on the new set. And of course, leave some free space for new route via points if you're going to want to do any route planning whilst on the move. The number of Via Points attached to each route is displayed in the Route tab box in MapSource after the route name, length, time and course, and you have to add them up here to check you're within limits.
We got the email from Garmin support too late for our trip and had to rush out the night before our departure to buy a new unit. But all was not lost because we managed (somehow!) to return the new unit and get our money back, and our old unit is happily reset and working a treat again.
Finally, when downloading data to your Quest from Mapsource, it is advisable NOT to press any buttons on the Quest at all until it has switched itself off after the transfer - I think this is where we went wrong and froze the unit because whilst downloading, the Quest came up with 'Route Waypoint Memory Full OK' and we pressed OK before the download was complete.