626 stalling

How old is the battery? It may have an internal short that is taking too much of the output from the alternator leaving very little to run the rest of the car. Try another battery. If the current one is out of warranty, it also means it is an old battery. You can also have the cells of your current battery tested, but if the battery is the original one or an old one, just splurge a bit and replace it and see what happens. It'll cost you less than a diagnostic visit to the repair shop anyway!