[Steve Tinker]

Do you have a multi meter - even a cheap one? If so proceed as follows - its not too difficult:

1) Check the battery voltage across the terminals - should be +/- 12.6v fully charged.
2) If less than 12.6v (which I suspect - it sounds like the battery has lost a cell) then the battery requires charging. Driving for 30 minutes is NOT enough to charge the battery fully - it requires 6-8 hours on a battery charger. If the battery still won't hold 12.6v after charging it needs replacing.
3) To quickly check the alternator, with the engine running attach multi meter across the battery terminals and check voltage - it should read 13.8 - 14.5v @ 1500rpm. Anything less than 13.5 and the alternator / voltage regulator is suspect.

These are just quick checks just to verify its something simple (like a new battery required) before giving the car to a repairer which can = big $$$.