A car can usually run several hours off the battery even if the alternator isn't working. If it runs once you charge the battery and then slowly stops working again, I would suspect something about the alternator - perhaps it wasn't connected correctly, it isn't working properly, open wire, etc.

If you have a way to measure voltage*, you can tell pretty easily. The battery voltage should be in the 12.5 V range before you start it, and jump up to something around 13.5V when the engine is running and the alternator is charging the battery. If it stays around 12.5V (and especially if the voltage slowly drops as it runs), then its the alternator (or something related to the alternator).

*you can unlock the instrument cluster - one of the built in test functions is to display voltage - search for instructions on this. A volt meter works just fine, too, you can measure in the engine compartment.

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David.X5
2001 X5 4.4i Sport
SOLD! at 160k miles