from your question it's not clear what order you disconnected the components---but the battery must be disconnected first.
My understanding is that if you pull the LCD connector before disconnecting the battery, that creates a sudden drop in voltage which will correspond to a sudden increase in amperage which blows the filter. I know that you mentioned that you didn't have the iPad powered on, but in the work of removing the screen, you may have pressed the power button at some point?
jessa