B737 CREW FLIES COMPANY FILED RNAV RTE PROHIBITED BY MEL.

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WE ARRIVED AT THE ACFT AT PDX APPROX 10 MINS PRIOR TO SHOW TIME; SO WE WERE NOT RUSHED. 3 MEL'S WERE LISTED FOR THE AIRPLANE (APU INOP; AUTO PRESSURE CONTROLLER INOP; AND #2 DME INOP). I BEGAN MY FO PREFLT WHILE THE CAPT DID HIS PREFLT AND REVIEWED THE PAPERWORK (LOGBOOK; RELEASES; ETC). PRIOR TO ENG START; THE CAPT AND I DID DISCUSS THE START PROCS WITH AN APU INOP (WE EVEN REFED THE QRH BLEED AIR DIAGRAM SINCE NEITHER OF US HAD DONE THIS TYPE OF START IN QUITE A WHILE); AND QUICKLY MENTIONED THAT THE PRESSURIZATION SYS SHOULD WORK OK IN 'ALTN;' AND THAT THE #2 DME WAS INOP; BUT DIDN'T LOOK INTO THE OPC MEL PAGES FOR THOSE ITEMS. THE FLT PLAN HAD US FILED AS A '/J;' BASICALLY MEANING NO RESTRS FOR THE RTE THAT WAS FILED. ONCE WE WERE AIRBORNE; THE CAPT LOOKED AT THE MEL FOR ANY AMPLIFYING DATA ABOUT OUR #2 DME MEL AND FOUND THERE WAS A NOTE 'RNAV NOT PERMITTED.' I WAS THE PF WITH THE #2 AUTOPLT ENGAGED IN LNAV; FLYING THE RTE BTWN PDX AND SJC. AS FAR AS WE COULD TELL; THE ACFT WAS STAYING ON COURSE (RNP ON THE LEGS PAGE OF THE FMC WAS STAYING AT ABOUT 0.23); AND WE HAD NO CALLS FROM SEA OR ZOA ABOUT ANY COURSE DEVS (THERE ARE NO BACKUP NAVAIDS FOR THIS ROUTING). THE CAPT REFED HIS FOM TO SEE WHAT THE GUIDANCE WAS ABOUT RNAV VERSUS LNAV (WERE THEY THE SAME? SHOULD WE REALLY BE FLYING IN LNAV WITH THE #2 DME INOP?) AND IT REALLY WASN'T CLR TO EITHER OF US. WE CONTINUED ON OUR ROUTING; WITH THE AUTOPLT ENGAGED IN LNAV UNTIL WE RECEIVED VECTORED FOR OUR APCH. ON THE GND IN SJC; THE CAPT TALKED TO DISPATCH AND MAINT CTL AND WE CONTINUED TO OUR NEXT CITY WITHOUT USING LNAV (RECEIVED HDGS TO VORS ALONG THE RTE) SINCE WE WERE NOW DOWNGRADED TO A '/W.' MAINT PERSONNEL THEN RETURNED THE #2 DME TO A NORMAL OPS. AS THE FO; I NEED TO BE MORE PROACTIVE IN CHKING ALL THE AMPLIFYING DATA ABOUT ALL THE MEL'S WE'RE CARRYING. THE CAPT I FLEW WITH WAS VERY CONSCIENTIOUS; AND WE DID HAVE GOOD CREW COM; BUT EACH PERSON CAN BECOME 'CHANNELIZED' AND I SHOULDN'T HAVE ASSUMED HE HAD RECEIVED ALL THE INFO FROM THE DISPATCH RELEASE WE NEEDED. THERE SHOULD BE SOME TYPE OF A CAUTION NOTE ON THE FLT RELEASE FOR ANY RESTRS THE ACFT HAS WITH A NAV EQUIP LIKE WE ENCOUNTERED (IE; 'LNAV/RNAV NOT AUTH FOR THIS FLT UNTIL #2 DME MEL CLRED.').