factory amp is garbage, bypassing it to use an aftermarket HU's amp is a good decision.
First, the HU should be on it's own power source. I actually run a dedicated fused wire myself as I won't have any doubts that way that it was done right.
That said, check all your connections one more time, and if the problem persists, you may be one of a select few of us who ever had a bad Alpine product. Exchange it asap.