was it no sound at all or just weak sound?
try jiggling some of the wires around inside with your fingers while its plugged in. if there is a pop at all, it might just be the positioning of the plugs inside. try strumming it again after that.
try getting another battery. theyre about $7 for a pair of them. you dont know how long that battery was in your uke before you bought it. maybe it was just on its last leg. it should be a 2032 sized battery.
other than that, unless i was able to actually take a look at it, couldnt tell you. i have had to "repair" two of the pickups i have because of poor workmanship... ie too much solder on contact points, poor insulation on wiring causing exposed wires to cross currents, etc etc...
if youre not comfortable with dealing with electrical issues like this, you might want to take it to a pro to have em look at it.