Push the release latch on the connectors and gently wiggle the connector back and forth to free them up. Most have a rubber seal inside and those can get snug over time.

A little finesse goes a long way with these connectors. I try to avoid he ECM connector if possible.

 

That's was a useless, toolbag comment, man.

 

Looks like the strap that is on mine. Does not go completely around the battery but lies underneath it allowing you to pull up on it and help remove the battery.

As far as removing the wiring to get to the battery, I just pushed the two main tabs (front and back) of the plastic doohickey they are attached to and pulled the plastic and wiring out of the way. Then, two torqs headed bolts removed on the battery cover to get it out of the way. Then pulled on the above mentioned strap at the back and fingers at the front and the battery came right up, after removing the battery cables of course.