What was found
AFTER A NORMAL TAKEOFF AND INITIAL CLIMB, THE PF CALLED FOR GEAR UP. PM SELECTED GEAR UP, BUT NO RESPONSE FROM LANDING GEAR. ALL 3 GREEN DOWN/LOCKED LIGHTS REMAINED ILLUMINATED, BUT THE RED GEAR UNLOCKED INDICATOR WAS ALSO ILLUMINATED. THE GND IDLE ANNUNCIATOR REMAINED ILLUMINATED AND THE CABIN PRESSURIZATION BEGAN TO FLUCTUATE, AS IF AN OUTFLOW VALVE WAS OPEN. ALL INDICATIONS THAT THE AIRPLANE STILL THOUGHT IT WAS ON THE GROUND. WE RECYCLED THE LANDING GEAR HANDLE BACK DOWN, THEN UP WITH THE SAME SYMPTOMS. WE LEVELED OFF AT APPROXIMATELY 3000' MSL AND ADVISED ATC THAT WE HAD A LANDING GEAR PROBLEM AND NEEDED DELAYING VECTORS TO GIVE TIME TO RUN THE CHECKLIST AND TROUBLESHOOT. WE COMPLETED THE LANDING GEAR WILL NOT RETRACT CHECKLIST WITH NO CHANGE TO THE CONDITION. AT THIS POINT WE ELECTED TO DO A LOW PASS BY THE TOWER TO VISUALLY CONFIRM ALL LANDING GEAR WERE DOWN, EVEN THOUGH WE STILL HAD 3 GREEN INDICATORS. WE COMPLETED THE LOW PASS AND TOWER CONFIRMED ALL 3 GEAR APPEARED IN THE DOWN POSITION. WE ENTERED LEFT TRAFFIC ON RWY 02 AND MADE A NORMAL LANDING WITH NO FURTHER ISSUES.