van keeps dying any advice greatly appreciated

[deanlad1980]

I have an 03 1.9 berlingo 120000 miles on the clock, was driving to work the other day and all of a sudden she just died no warning lights or anything,had plenty of fuel in her, but battery was dead.

Put on a new battery fired up straight away, but 10 minutes down the road she died again with a flat battery, again no warning lights or smoke etc.

Towed her home and put a multimeter on terminals (with a charged battery) getting 12.5v not started and 14.2v when started.

when running if I put the window de-icer on can hear the strain on engine, but 14.2v leads me to believe the alternator is fine?

Im completley baffled and have tried 3 seperate batterys

Help before i put her out of her misery