BMW Repair: 2001 bmw 325 Cic, open heart surgery, master mechanic

Question
Hi:
I had bought a used 2001 325Cic from a friend's mother car that had been
sitting in the garage for the last 2-3 years. the car had been to the bmw
dealer for oil change late as dec 2007, and was able to drive 2 weeks before i
arrange to pickup the car. when i arrive at the garage, the car wouldn't start.
the key ignition only able to light up the dashboard and head light and not
even a sound of engine rev up.i had the jump start with the battery
connection in the back( trunk). and the car then start and able to drive for 30
minutes an it start dying. i notice the oil light , engine, brake... on the panel
lighted yellow . the engine feels like loosing power and stepping on gas only
able to go at 30 mph ,and finally at the stop light the car engine stopped.
another jump start attempt with a pickup truck from the front engine
connections, the car start but would not hold the charge to continue and stop
the second the cables are removed. car then was told to local Firestone
mechanics who were able to change the battery although not to the exact
size of a bmw but there were plenty of power, but they could not get into any
voltage into the circuit for the diagnostic read out . So the car then eventually
tolled to the dealership where  a battery and a alternator were replaced , and
it was reported fine .  
can i rely on that assestment since i would need to travel 400 mile to pickup
the car and be assured to drive home. what if the car dye again and the local
cannot service it? why was the system not allow the Firestone master
mechanic to access into the computer program to check or reset the
modules...
any prevent advise to ease my mind before the trip would be grateful and
appreciate.
Ben

Answer
Fix of alternator sounds appropriate.

Why wasn't the Firestone mechanic able to fix?  Same reason I didn't let the Walmart pharmacist perform my open heart surgery.

BMW mechanics go through a very extensive BMW-only training.  A firestone mechanic can't be expected to know the same level of detail, though I'd admit I would hope one could have diagnosed this.