your fuel pump should be in your gas tank..
you have to remove the tank from your vehicle then open the ring on top of your tank then the disk can be lifted out of the tank and your fuel pump is attached to that disk.
P0700 is just the TCM telling the PCM to turn on the check engine light because it sensed a problem in the transmission. The code P1776 is most likely a complete valve body replacement issue, About $1000.00 for parts and fluid will be about $25 plug a filter and gasket about $25 more. Before you do anything have this professionally diagnosed, don't guess, which is what I am doing..
May have a blockage in the cooling system. Issues with the fans not working properly. Air still in the system bad radiator cap not holding proper pressure. Lots of possibilities