Any ideas on this...

At the moment my S80 2.4t wont start because the battery is dead (that's straight forward)... the thing is... when I try to jump start it with my other car, while the jump leads are connect to it, it starts and idles comfortably as if there is nothing wrong at all but... as soon as the leads are disconnect from the other car, the engine from the S80 dies... The clocks and the warning lights on the S80 don't work (I know about this issue) but in the past has not stop the car from running and driving smoothly (this is the reason the car has not arrived at the garage as yet)... now the outcome of my method of thinking would suggest that perhaps the alternator may be at fault here as it is instrumental in charging the battery... could this be the case or am I missing something?