No it won't. Not sure what you mean by "starter module", but the fuel pump should only run for one second after turning on the ignition switch, then again during engine cranking. The fuel pump must never turn on with the ignition switch in the "ACC" position. If it does, you have a severe fire hazard.
DrCranknWrench is right about testing the battery before you go looking for more complicated stuff. Watch what happens to the brightness of the head lights or dome light when you try to crank the engine. Also, if you hear a single, rather loud clunk each time you turn the ignition switch to "crank", the contacts in the starter solenoid are worn. That is a real common problem with a real easy and inexpensive fix on the little silver Nippendenso starters, but that always starts out as an intermittent problem that gives you months of warning as it gradually gets worse.
Thursday, March 29th, 2012 AT 3:42 AM