I too have a 2001(.0) Pathfinder that cranks but won't start. I bought it used, not running. It had been sitting up a year or more; dead battery, out of gas, leaky sunroof, moldy interior. Now that I have replaced the battery, added anti-corrosion rings, shims and gel, she tries really hard to crank and almost will via starting fluid. The Security diode flashing when on. Both the Security light and SES are on steadily with key on, even after attempts to reset (ON 5, OFf X 3, disconnect battery overnight, erase codes). All the fuses are good.
I cleared the one CONFIRMED code, P1131 by replacing the swirl control solenoid valve. The old one read as on open circuit. A mechanic recommended replacing the fuel pump since it was apparently getting spark, contending that the immobilizer was therefore not interfering. The pump is capable of generating 40psi in the fuel line without the car running. I've read elsewhere that the NVIS system DOES in fact control the fuel injectors, so I've left the fuel pump as is for now.
I have PENDING P1610 - Lock Mode and PENDING P1615 - Difference in Key. I do have both original keys and both working fabs. I have downloaded the factory service manual form this site, and followed the diagnostic procedures as fair as I can, substituting my Actron CP9575 AutoScanner for the Nissan dealer's CONSULT. The Nissan service advisor quoted $69 just to look at it, $110/hr diagnostic time if it takes them longer than 30 minutes to diagnose, $105 for reprogramming, and pointed out that if units are bad the cost could run into the thousands. If I hire them to install their expensive components, the diagnostic fees MIGHT be waived, but if I try using parts from other sources I could very well end up paying more in the long run.
I've pretty much narrowed it down to the IMMU (Seimens 28590-C9917). I suspect it has a bad antenna, is not capable of linking either of my two original keys to the ECM. I can send the ECM to be tested for a flat fee of $20. They can test the IMMU as well (possibly for another $20, not sure). A new IMMU costs $208 plus labor from the dealer, $117 at the local parts store, $30 for a used one on eBay, or $10 from a junkyard if I can find it out there myself.
The Nissan service advisor insists that whatever IMMU will have to be reprogrammed. Nissan's Procedure 7 (EL-370. 371) for P1610 - Lock Mode says to make sure it is installed correctly (pretty simple, one plug and one bolt); if it is, try reprogramming it. It that doesn't work, then try another original key; no luck, replace and reprogram the IMMU (EL-366). In that the first reprogramming would occur as a required part of the diagnostic, it would be bothersome to be expected to pay an additional fee if that required step in the official diagnostic solved the problem (if my IMMU was ok and all I needed was a reflash). For all I know, all I would be charged for is the $105 reprogramming. I'm probably overly optimistic to think I'd get by for only $69. I just don't know. I would prefer to avoid the scenario where I am charged diagnostic time plus two or more re-programmings because I'd prefer to save $90 plus labor on a new part, or save more with my junkyard treasure hunting.
The seller on eBay claims his friends say tell him the replacements work fine with no need to reprogram the ECM (but he was quick to point out that he does not know the particulars of my problem). I'm just going to see if I can find the part in the junkyard, buy it, install it, do the 5sec x 3 reset sequence and see if my Pathfinder will simply fire up. And I've already ordered a little $15 oscillator kit off eBay so I can test whether a signal is being sent between either IMMU and my ECM if need be (Procedure 2(8) EL-364

That ought to give me a better idea of which IMMU to have in place if and when I do have to haul it to the dealer, or a locksmith.
Any insights out there on whether an IMMU for a 2001 Pathfinder has a long term memory, one that might be affected by prolonged loss of power perhaps? Or is it essentially an antenna and decoder ring? Or something in between, like a short term memory used each go-round?