I do not believe the AAZ has any fuel pump other than the injection pump on the engine. The injection pump serves double duty for both pulling the fuel from the tank and pushing it through the injectors and into the engine. Adding a lift pump can sometimes help, although that help is often in the form of covering up other issues, and without a lift pump the engine should start and run fine. There are a slew of reasons that can cause hard starting. Here's a non-exhaustive list: injection pump lost its prime, fuel filter lost its prime, poor injection pump timing, poor cam timing, mediocre battery or connections, mediocre starter or connections, bad glow plugs (even one bad one makes a big difference), no current to glow plugs, the simple act of forgetting to pull the cold start, bad lifters, clogged air filter, bad fuel, bad injection pump, etc, etc, etc...