iPod showing empty battery icon with fully charged battery

My iPod turns on with a charged battery only to show the empty battery icon and turn off. The iPod wasn’t charging through the dock connector but turned on if a charged battery was connected. A few days ago I was using a multimeter and managed to turn on the iPod connected to the charger, the iPod turned once then shorted. After some testing the IPod turned on to show the empty battery screen, while turning on the logic board overheats near the front assembly connector. After some testing with the multimeter I came up with a few ideas:

1. The short is caused by a faulty chip or diode that handles power distribution. Possibly one of these: U3 (below LB), Q4, Q3 (upper LB, near the front assembly connector)

# (This is where the logic board overheats)

#

1. The iPod only recognizes original batteries, when I tried using a replacement battery (850Mah) it stayed off.

# I replaced L3 and resoldered L45 (both of them showed fractures) and both seem ok but the iPod still doesn’t charge (although the logic board receives the 12V from the charger).

I would like to know how could I spot a faulty component, especially the ones which handle the battery power, since I have at least other two shorted 3Gs for spares, it seems to be a common problem for this model.

On another iPod I would simply replace the LB, but I would really like to fix this one since it was a gift and holds a big place in my collection (all my other iPods were purchased).