Starter replacement instructions

Get in the and start it let it run a little. Go to the store turn it off when you come out to start it it won't turn over. Lights and all power works but won't crank over. It's done this a few times every time I go some where. It would start it after thirty to forty minutes. Now it won't turn over at all. Had it towed home and the tow driver thinks it's because the driver side door will no let you lock it with the key. You can unlock the car but will not turn to look the car doors. He thinks because you can't lock it with the key the alarm kicks in that keeps it from turning over. And some people say it's the fuel pump.
Any input would be appreciated!