Testing continuity at battery/logic board.

I changed the battery in a 2G 16gb iPod Touch that I bought as non working. Looks like the guys father who soldered the battery could have done a better job... but....

I installed new battery and it started but only to the apple logo boot screen... over and over. It also ran pretty darn hot at the back lower left corner.

iTunes could see the Touch but any Restores failed. Still ran hot. New battery started to go low quickly (a few hours of attempted restores...HEAT).

Left it plugged in over night. Never started again. No more heat ;) Meter reads 3 volts. Before install new battery was 3.7.

Question...

When battery is installed in Touch a continuity test between the two outer leads (+ -) beeps (they are "connected"). I did this test on 3 diffrent batteries (2 old/1 new). 2 of the batteries beeped/showed they were "connected" 1 did not.

Question 1.2...

Is it normal for pos and neg leads of installed battery to show continuity?

Thanks.