When there is no battery connected to an iPhone, and you plug it in to the wall, or computer, the Apple logo should display for a few seconds, and then go off, and then come back on, then off, like a boot loop, as it can't see the battery, so won't boot.
So, if you're not seeing the Apple logo when it's plugged in, then you may have likely damaged something else, you may have damaged something else if you have damaged the battery connector on the board, you must've been prying hard to break that off though. :-)