from what you are saying the following happens
you turn on
you can hear the compressor start but about 10 secs or less later there is a click and it stops
if you wait a while the compressor starts up but again 10 secs or so later it stops
if above is the case then you have a compressor or starter issue. this may be a faulty starter but more often than not its a faulty compressor. If the compressor has failed then you need a new fridge
the only way you can find out which is to fit a new start relay. A proffessional would carry test components he can plug in to test and remove again. If you did it you are dealing with a make that is not easy for sprares at the baes of times
hopefully one of the fridge engineers will add to this the likleyhood of the compressor being the fault
Dave