Flight Crew Air Transport Pilot (ATP); Flight Crew Instrument; Flight Crew Multiengine
Flight Crew Total 20000
Aircraft Equipment Problem Critical; Deviation / Discrepancy - Procedural Published Material / Policy; Flight Deck / Cabin / Aircraft Event Smoke / Fire / Fumes / Odor
Flight Crew Landed in Emergency Condition
Aircraft
Nearing top of descent; the ISFD quit and displayed OUT OF ORDER. Descent began and passing approx 12;000 feet; received call from cabin that they smelled smoke. The smell was of a burning smell; similar to burned popcorn. It was prevalent in rows 10-14. I confirmed that no smoke was actually present just the smell.  We adjusted the packs cooler and the smell dissipated. We had [Runway] XXL in the FMS and received a change to [Runway] XXC. While trying to load [Runway] XXC into the box we found that both FMSs would only show [Runway] XXL and no other approaches would populate on the arrival page. We then received another call from the cabin reporting that the burning smell was back but no smoke present. With the ISFD having quit; the FMS anomaly suddenly present; and more burning smell present; began to think we had a melt down of some sort going on in the E & E compartment. [Advised ATC] stating we wanted [Runway] XXL since we couldn't as yet make out the field through the scattered clouds below us and couldn't select any other approach. Fire trucks gave us a once over and followed us to the gate. Kept the flaps at 40 just in case an evac was necessary if smoke began to fill the cabin. Burning smell persisted on the ground to the gate but no smoke was present. Had pulled the Smoke; Fire; Fumes Checklist out but I decided the most prudent and efficient act was to land ASAP and elected not to execute this checklist while on an accelerated final approach with no smoke present in the cabin. No FA or passenger needed medical attention. We never smelled smoke or a burning smell in the cockpit.Post flight maintenance found a bad light ballast in the vicinity of rows 10-13.  The ISFD failure and FMS anomaly were apparently unrelated but had occurred rather simultaneously.With more time; say if we'd been at altitude; the Smoke; Fire; Fumes checklist could have isolated the problem and may not have led to the interpretation of a more serious situation possibly developing.
B737 Captain reported a cockpit display failure with an unrelated simultaneous cabin lighting ballast failure resulting in a precautionary landing due to suspected electrical fire.