thick oil due to late service new engine required

Hi,I was late for first service with my diesel mini,,38000 miles during which I kept oil at good level.Im told by the garage that the late service has turned the oil to thicker than treacle,and this has caused me to need a new engine,,,,is this normal?,,,I have a four stroke lawnmower that has never been serviced in 4 years and its ok.they say the man hours required to clean it all up would cost more than a new engine,any advice on this would be welcome and appreciated
Thanks
Bill