Checking with the schematics of shield (v3.0) there’s no way it could short the inputs.
There’s always some kOhms in all points that goes to ground, so even killing transistors on shield won’t make it short the inputs.
Well, unless your exact board assembly was faulty from the factory 
But maybe there’s something wrong on your sketch side.
Check that you’ve configured arduino ports to push-pull output mode, and not as open drain with internal pullups.
The pull up resistor will allow you to see output levels when not loaded, but when loaded with led (as on the relay shield), the voltage will drop.
And it won’t be able to output enough mA to open the relay driving transistor.