well I guess the problem starts at the pump....I suppose hard wiring a pump you know is good would be the next best step, if that works try to hook it up. If that doesn't work, you needed a new fuel pump anyway, and the other problem is the relay or the wires...hopefully...
As for the light staying on, I don't remember for sure but I think it means it needs a new one....I suppose I'm not sure how far you've dug into the problem, so hopefully I'll be of some help to ya..