B737 CREW HAD ALT OVERSHOOT WHEN THEY REALIZED THE AUTOPLT WAS NOT ENGAGED.

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FLYING THE POM 6 DEP FROM ONT TO OAK IN BRAND NEW B737-700. ESTABLISHED ON 255 DEG HDG TO INTERCEPT POM 114 DEG RADIAL INBOUND AND CLBING AT 3000 FPM; I SELECTED 'LNAV' AND 'V SPD' ON THE AUTOPLT MCP AS I TYPICALLY WOULD DO. APCHING 7000 FT MSL; I NOTICED ON MY EFIS DISPLAY THAT 'ALT ACQUIRED' AND 'LNAV' BOTH WERE ANNUNCIATED; BUT WE HAD DRIFTED L OF THE 255 DEG HDG. THE NEXT THING I NOTICED WAS THAT THE AUTOPLT WAS GOING TO OVERSHOOT 8000 FT LEVELOFF. ONLY NOW DID BOTH THE CAPT AND I SIMULTANEOUSLY REALIZE (AND CONFIRM VISUALLY -- NO GREEN LIGHT ON 'AUTOPLT B' SWITCH) THAT THE AUTOPLT WAS NOT ENGAGED. I WAS NOT ABLE TO STOP THE CLB UNTIL WE REACHED 8300 FT MSL AND SOCAL CLRED US TO 9000 FT AND DIRECT POM TO RESUME THE DEP. I SUSPECT THAT I NEVER DEPRESSED THE COMMAND AUTOPLT B BUTTON; EVEN THOUGH MY BRAIN WAS ASSUMING I HAD SINCE I WAS SEEING THE FLT DIRECTOR STATUS INDICATOR LIGHTS ON MY EFIS PANEL AND MISTOOK THEM FOR WHAT THE AUTOPLT WAS DOING. (WE HAD TOGA MODE ENGAGED FOR DEP; SO THE FLT DIRECTOR WAS ALREADY ALIVE.) CONCLUSION: RELATIVE UNFAMILIARITY WITH A COMMON TYPE-RATING ACFT; YET RADICALLY DIFFERENT LOOKING PRESENTATION CONTRIBUTED TO THIS SIMPLE ERROR OF OMISSION. ALSO; YOU REALLY HAVE TO PUSH HARD ON THE YOKE AND PULL OFF NEARLY ALL THE PWR TO MAKE THIS BEAST STOP CLBING! THE FAMILIAR 'SCORE BOARD' OF THE -300/-500 AIRPLANE LOOKS A LOT DIFFERENT ON THE -700. I HOPE NEXT WK WHEN I'M FLYING THE B737-200 I WILL REMEMBER THAT IT WON'T LEVELOFF ITSELF REGARDLESS OF WHICH BUTTONS I PUSH OR LEVERS I ENGAGE.