120i wont start!

Hi,

I'm new here and need some advice and I'm not a huge car buff and therefore do not know much about cars mechanically. I bought a 2009 120i last week. I went to pick it up on Wednesday from the dealer and it wouldn't start. They blamed it on the service guys having the doors open for 4 hours while they were detailing it. They put it on the trickle charger and said the battery was run down but holding charge and appeared fine. On the safe side they did replace it. I have had it for 24 hours now. Today the battery light appeared and disappeared after half an hour of driving it as well as the cruise control fail light came on.
I drove it a few hours later for 30 Km. Parked for about 3 hrs and then went to start it but again it would not start!!!
Had the roadside assistance out and was told the battery was faulty and couldn't take charge. The alternator was fine. So driven it home after a jump start but obviously can't start it now!
Went over the pits on Tuesday and came back with no obvious faults.
Obviously couldn't call the dealer today as it is Sunday but will call them tomorrow and give them a piece of my mind.
Would this be a battery cable fault like in the 5 or 6 series? Would appreciate any advice!