2001 Range Rover Shuts off and on while driving

I have a strange problem with my car and even my mechanic doesn't know where to start to look.
It happened first on the tnpke freeway at the speed about 80 m/hr after 1 hr of driving: the arrows on the speedometer and thochometer started to
jump up and down and suddenly dropped to 0 completelly, but the car continued to drive at the same speed without any noise or shaking and in a while
the arrows got up again and there was no problem to the end of the ride for another 1.5 hr.

Next day on the way back it happened again, only this time after driving with arrows on the 0 for five minutes the car shut off completelly and couldn't start.
No spark, nothing. But in a few minutes it got power on again and drived another 40 minutes with no problem.

Next day I called the towing truck and took it to the Land Rover dealer, they put it on the computer and it shows a few minor problems which couldn't couse
the problem. They said that the battery is old and replaced it. On the way home after 40 min. Driving the same thing happened again and the car shut off and
couldn't be started again at all.

I called the tow truck again and took it to another mechanic who specializes in foreign cars, but he doesn't know where to start to look. The car doesn't power
on at all, and he can't see how it all happened.

Can someone help please, or maybe someone can recommend a mechanic who really knows Range Rovers in Miami area?

Thanks a lot!