1998 Infiniti I30 Question: car will not start at random times - then starts fine for a week

Intermittent faults can be so hard to find. I hope they have tested the battery and made sure the cables are clean tight and secure I would be looking for a voltage drop or bad electrical connection in the starting circuit/ignition switch and starter itself. When the car wont start I would get someone to crank the car and measure voltage across the battery, it should be 12.6 volts at rest, above 10 on cranking. With the car in neutral or park when the car won't start try putting a jumper wire from the battery (+) to the small terminal on the starter and see if the starter will crank over at normal speed. You need a good volt/ohm meter and wiring diagram to get to the source of the problem. Autozone have some popular workshop manuals for free on line once you register (for free) on their website http://bit.ly/autozone_repair_info.
and get an online repair manual subscription.
There is a company that independent auto repair shops buy their information from that the same information inexpensively to do it yourselfers. The information is year make and model specific repair procedures, service bulletins, component locations, wiring diagrams ect.... Alldata is very easy to navigate http://bit.ly/AllData_Repair_Manuals_Online