Where did batteries come in? where is 3Ah from? The OP didn't mention batteries or Ah
Setup was
"I connected my 12 volt 3 amp bilge pump to a 36 watt 3 amp 110v ac/12v dc power converter."
It should work fine if (as said in previous posts)
1. The converter is actually outputting 12V DC when 3A is drawn
2. The pump is only drawing 3A
An old pump may have bearing issues, causing it to draw more current, for example.
As also stated previously, it is possible that the pump may draw a lot more when it is first switched on. The current surges, drops the voltage, the motor stalls, continues to draw too much current, and continues to stall.
But, that is not terribly consistent with the impeller blade vibrating and not moving (could be though).
If you connect the pump to a 12V battery, does it work? (maybe the pump has an issue, which would be more consistent with it vibrating).
If you (very carefully) assist the motor, does it get started?