The pump itself on my F4i works fine. Power isn't going through the wiring interface where the wires go into the pump assembly. I've provided pics.

http://imgur.com/gallery/tRrrPM8

How can I rebuild that part? Melt the connection with a soldering iron or torch? Is there a way to take it apart?

I'd rather fix it than buy a used pump because 1) people want over $200 for them used, and 2) the pump assembly works fine otherwise.

 

Fixed. All it took was slightly bending where the wires went into the fuel pump assembly.