I'm having issues with my vehicle's fuel pump system, and I can't
really figure out what's going on.

A few nights ago, while rounding a corner, my car shut off completely
and would not start thereafter.  I purchased her a few weeks ago and
was told she was "cold sensitive," meaning that I should let her warm
up for a few minutes before driving, and had noticed that, within the
past week, it seemed to take a lot longer for the car to "warm up."

After inspecting the spark plugs and distributor coil and that stuff,
I've discovered that those are fine.  I've done some reading and found
that "cold sensitivity" in my model of car usually means that one of
the fuel pumps is out and the car is only running on one, which made
me think that the one it was running on finally gave out.  So, I
removed the rear fuel pump to discover that it was completely dead.
I've gotten a new one and put it in, but there's almost no current
traveling back there to power it.  When tested at the battery where
the current is strong, the pump runs.  But not in the back, where the
current is considerably weaker.

Where do I go from here?