A dead short = infinite current fuses blowing or wires melting - you do not have a dead short.
Can you be sure that the alternator is actually working - if it is you should have about 14V across the battery terminals on a fast tickover.
Sometimes the "battery charging" lamp fails - the alternator depends on this bulb to be working to be able to generate power to charge the battery. Blub should light up with engine stopped and gradually go out as revs increase. A blown lamp would cause the symptoms you report.
Good luck...
Peccavi
April 2010
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