C560 DSNDING INTO DEN IS UNABLE TO ADHERE TO PUBLISHED XING ALT BECAUSE OF PROGRAMMING DIFFICULTY.

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PART 91 IFR ON THE QUAIL4 STAR TO APA. ZDV CLRED US TO CROSS QUAIL AT 12000 FT. THE PF PROGRAMMED THE VERT NAV MODE FOR THE RESTR. I WAS UPDATING THE ATIS AS THE WX WAS DROPPING RAPIDLY. THE PF TOLD ME HE WAS HAVING A PROB PROGRAMMING THE VNAV MODE; SO I BEGAN TO HELP WITH THE PROB. THE SYS WAS SET TO CROSS THE DEST ARPT; NOT QUAIL AT 12000 FT. I BEGAN TO REPROGRAM THE VNAV CORRECTLY WHEN THE ZDV CTLR ASKED IF WE WERE GOING TO BE ABLE TO MAKE THE RESTR. AT THIS TIME WE WERE LEAVING FL240; 3 MINS FROM THE FIX. WE SAID NO BUT WE COULD COME CLOSE. THE CTLR TOLD US HE WOULD CHK IF DEN TRACON COULD 'TAKE THE HDOF' THE NEXT XMISSION WAS FOR US TO CONTACT DEN APCH. ON CALL UP I RPTED OUT OF 14500 FT FOR 12000 FT. DENVER APCH TOLD US TO TURN R IMMEDIATELY TO A HEADING 350 DEGS AND TO MAINTAIN 14000 FT. WE WERE AT 14100 FT; AND LEVELED AT 14000 FT. THE TCASII SHOWED A TARGET THAT WENT FROM 9 NM TO 6 NM AT 11 O'CLOCK POS; 1000 FT BELOW. NO TA WAS RECEIVED. WHEN WE WERE CLR OF THAT TFC; WE PROCEEDED NORMALLY TO LAND. I THINK THE PROBS WERE DISTRS CAUSED BY THE AUTOMATION AND WX LEADING TO A LOSE OF SITUATIONAL AWARENESS OF OUR DISTANCE TO THE RESTR AND ALT TO BE LOST. SOMETHING THAT CAN BE DONE BTWN THE EARS; AS WELL AS WITH THE 'BOX.'