I tried to erase the non-volatile memory.

When I started up, the time in the top middle was "2:10", but a few seconds later the wrong time came back:
9:10 12 janvier 2006.

I'm going to wait for the battery to discharge completely (leave the GPS on, then wait 2 or 3 weeks).
There's no screw to remove the back cover, so I can't remove the battery myself.

I'll let you know the result in a few weeks.