The Tiny Lili might have a short
-Make sure the battery has a good charge.
-Connect a small motor to the battery to see if the motor runs and if the voltage drops. (this will give you an idea if the battery is good)
-Use an ohm meter to measure the resistance of the Tiny Lili (measure from power to ground, with power disconnected). If the reading is close to 0 ohm's then that would mean that the Tiny Lili is shorted.
I use the hot air gun to resolder those chips, just make sure you secure the Tiny Lili so that it doesn't blow away.