for 3000 i doubt they mean the remote, they probably mean the key with the ignition port. you might want to double check on that. as for programing no one besides the dealer can program an OEM key/remote besides the dealer.
this is a constant issue with your cars model and there has been an official TSB from infiniti in this very problem.
Service Bulletin #: ITB-09-037
http://www.allworldauto.com/tsbs/NHTSA_ ... 00845.html
not necessarily so don't jump to conclusions if its an aging issue, which most likely it is the electrics need some work.
i had the same issue since i didn't move my seat since i got the car, it could be just an electrical problem which in that case wont cost much, i fixed it for just 150 dirhams.