Bridge rectifier destroyed at power up
Yes, you cannot connect either of the DC terminals of the bridge rectifier to the mains ground. Remember, one of the two "active" mains inputs (usually called "neutral") is also tied to mains ground. This means that when the other mains input ("line") goes negative, it is forcing unlimited current through one of the diodes in the bridge.

Both sides of the bridge rectifier output must be allowed to "float" with respect to ground.