Hello, my name is XXXXX XXXXX I will try help you with this.
Most likely cause is either the charging system or the battery is at fault.
You might think because the engine starts that the battery would be ok but this is not the case these days. The battery has to deliver a lot more power to run many electrical systems. If it can't do this or the charging system is not working properly then the problems you indicate can occur.
To walk away from it would depend on what I was paying for it and its general condition.
Once the dealer repair it, it should be fine.
If the car had been on the forecourt for a while without being started then that could have affected the battery.
What you should do though is when the garage tell you it has been repaired is ask for a test drive in it with the mechanic that repaired it and make sure it is ok before you accept it.
The alternator is part of the charging system, not the only part. The system includes wiring, earth connections, charging light and sometimes maxi fuses.
thats wonderful mark thank you very much