Help! Battery or Alternator??? ~NEWB~

Since Monday, the battery in my 2000 528i keeps dieing (manu 06/00). Jump, drive, park, dead. Last night I checked the cells; they were a bit low (not to the plates). I refilled with distilled water and drove the freeway for 40 minutes.

This morning, battery dead again! Jumped it and drove the 6 or so miles to work. Shut down the engine and it restarted. That was at 8 am. It is now 2:30 pm, I went out to start the car and it is dead again. ARGH!

Called dealer. Battery $157.00 Diagnostics and install $120.00.

If I can get some diagnostic advice from the board, I can purchase and install battery (practically had it out to fill the cells last night).

The battery light is NOT illuminated on the dash. Is this most likely a bad battery or alternator?

Any advice???

Thanks in advance.

Probably the battery. Check to insure the belt driving the alternator is tight. Most any auto parts chains (AutoZone, Napa, etc) will test your charging system with a hand-held unit to determine for certain it is the battery, and rarely charge for the service to test it.
If the alternator has failed, the vehicle would not operate without electrical power. The battery's main function is to start the engine, once started, the necessary electrical power is generated by the alternator, including recharging the battery, presuming the battery is capable of being charged.

I thought the Bentley manual said the batt was maintenance free, but maybe I misread. Anyway if you have a DMM check voltage at the battery with the key on. Should be about 12v. With the car running it should jump to around 14. If it is at 14 or so running, your alt should be OK. You may want to check the current draw when the car is off. That should be about .04A or less (I think) but probably not your problem. You probably need a new battery now anyway, so I would just go get one. That is most likely your problem. BTW most auto stores will check out your charging system for free.

Thanks! Much Appreciated.