Fuel pumps require some retinkering when it takes more than one pull to start it. Basically, inside of the fuel pump are two clear plastic nickel sized diaphragms/valves. You flip the two clear plastic diaphragms over so that the smooth side is then in contact with the metal rim around it's edge. Currently, the flapping of those clear plastic diaphragms has roughened the face that contacts the metal rim. This roughness causes a poor seal and poor pressure that produces the fuel flow.
You might also disconnect the temperature sensor and stick a bare wire into each contact of the end of the connection that you just separated. This takes a possible defective sensor out of the loop, which would otherwise keep the engine from starting or cause it to run poorly as it warms up.