I can't guarantee your fault, but i know mine had a very similar fault. It wouldnt start perfect from cold, but you didnt have to crank it over for 5 minutes solid like you did when it was hot and you switched off to put petrol in (which got very embarasing on a daily basis )

Check for pressure, leave it overnight and before you even put the key in the ignition push the flap on the metering head down and it should rise back smoothly, if it springs back then it has lost pressure.

As a yard stick, after that prime the pump a few times and repeat the test.......thats the easiest way