Nissan Repair: 99 Maxima failure to start, backup key, remote start

Question
The car is a 1999 Maxima with every record from brand new.  I drove the car and started it a few times yesterday.  got home and shut it off for about ten minutes.  Got back in and no start.  It turned over good but no start.  I haven't checked for fire yet.  It sounded like a fuel pump to me.  It has a remote start installed.  I used that to check to see if the pump would buzz when the key was turned on.  When turned on, I could hear a slight buzz for 3-4 sec. ta the rear of the car.  I raised the hood and did it again, I could hear a simultaneous buzz in the engine compartment, so I don't know if it is telegraphing the sound or not.  The car has 121000 miles on it but has been running great and has been serviced regularly for everything.  The coils were replaced under warranty on a recall.  Would a fuel filter go that quick or would I have a warning?  Thanks for any help, I try to repair my cars myself and hope I can avoid a repair bill other than parts, but if it is the pump, I think it is in the tank, I probably can't do it.  I would like to know before I go to my mechanic.  Thanks again

Frank...

Answer
First use your other key to see if the primary key has gone out.  If the key is zeroed the car will not start.  If the backup key will not start the car you will need to let me know if the car turns over.  If the engine spins but will not start then it is the fuel circuit considering you say the coils were replaced under warranty.  You did not say if it had a check engine code?  I assume it does not and if that is the case you probably have a bad pump.  I have a 350Z and the fuel pump has already gone out on it.  So, do not be surprised if it is the pump.  You can check the fuel pressure to see if you have the proper pressure.