B747-400 CREW HAD AN ALTDEV AFTER A MISSED APCH IN IMC WX AT ORD.

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AFTER A GAR AT ORD; WE WERE LEVEL AT 5000 FT. THE AIRPLANE WAS ON AUTOPLT AND THE CAPT APPARENTLY AND INEXPLICABLY HIT THE TOGA BUTTON. THE ACFT STARTED TO ACCELERATE AND CLB. I ADVISED THE CAPT THAT WE WERE CLBING AND THAT WE SHOULD DSND. I NOTICED THE CAPT STRUGGLING WITH THE YOKE; AND I NOTICED THE AIRPLANE STILL ACCELERATING; SO I MANUALLY REDUCED THE THROTTLES TO IDLE IN EFFORTS TO HELP HIM DSND. ATC ADVISED US THAT OUR MODE C APPEARED TO BE MALFUNCTIONING. HE SHOWED US AT 6300 FT. I TOLD ATC THAT WE WERE DSNDING BACK DOWN. SUPPLEMENTAL INFO FROM ACN #567467: WE WERE ASSIGNED 5000 FT AFTER A MISSED APCH WHILE WE WERE MANEUVERING FOR ANOTHER TRY. THE CAPT HIT THE GAR SWITCH; AND THE ACFT CLBED TO 6500 FT BEFORE THE CAPT GOT CTL OF THE ACFT AND STARTED BACK DOWN. THE FO TOLD HIM TO DSND; BUT HE DIDN'T HEAR. AT THE TIME; HE WAS TASK SATURATED; AND WAS TRYING TO DO TOO MUCH HIMSELF AND NOT USING HIS CREW. APCH CTL RPTED THAT HIS MODE C MUST BE BROKEN; BECAUSE HE SHOWED US CLBING THROUGH 6300 FT. SUPPLEMENTAL INFO FROM ACN #567468: AFTER A GAR WITH THE CAPT FLYING; WE WERE GIVEN VECTORS TO A DIFFERENT RWY (RWY 32R); WHEN WE WERE GIVEN VECTORS TO INTERCEPT THE APCH. THE CAPT HIT THE TOGA SWITCH AND ENDED UP CLBING TO 6400 FT BEFORE BEGINNING THE DSCNT FOR THE APCH. OUR ASSIGNED ALT WAS 5000 FT WHEN WE WERE CLRED TO INTERCEPT THE APCH. APCH SAID 'CHK YOUR MODE C AND DSND.