CAPT OF A B777 MOMENTARILY LOST CTL OF ACFT DURING INITIAL CLB AFTER TKOF WHEN REACHING TO RESET; AND TURN ON; THE WX RADAR WHILE TURNING AND LOWERING THE ACFT NOSE TO ACCELERATE. WHEN HE NOTICED THE ACFT DSNDING; INSTEAD OF CLBING; HE IMMEDIATELY CORRECTED BY PITCHING UP AND 'FIREWALLING' THE THROTTLES. AT THE SAME INSTANCE THE GPWS WARNING SOUNDED.

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CHAIN OF EVENTS: WE HAD A MECHANICAL PROB WHICH DELAYED OUR DEP 45 MINS. OUR PREFLT SEEMED RUSHED AS OTHER PERSONNEL KEPT ASKING FOR INFO (LIKE THE FLT ATTENDANTS AND GATE AGENTS). TAXIING OUT OUR CLRNC WAS CHANGED AND INSERTED INTO FMS. THESE LED TO THE WX RADAR BEING LEFT OFF AS WE DEPARTED INTO RAINSHOWERS. THE CAPT WAS HAND- FLYING AND AFTER THE GEAR WAS CALLED FOR (UP); HE BEGAN A TURN TO THE TWR ASSIGNED HEADING. ABOUT THIS TIME WE WERE ABOVE OUR ACCELERATION HT; AND HE STARTED TO LOWER THE NOSE TO ACCELERATE. SIMULTANEOUSLY; WE ENTERED THE CLOUDS AND THE CAPT THEN WENT TO TURN ON THE WX RADAR. NORMALLY THIS IS AS SIMPLE AS HITTING A SWITCH ON THE EFIS CTL PANEL; HOWEVER; THE WX RADAR CTL PANEL WAS STILL SET IN TEST AND +15 DEG PITCH. SO; THE CAPT REACHED DOWN TO CHANGE THE PANEL ON THE AISLE STAND. UNFORTUNATELY; I ALSO LOOKED AT THE PANEL; BECAUSE WHEN I LOOKED UP; I SAW A DSCNT OF THE VERT SPD. I IMMEDIATELY CALLED OUT 'WE'RE SINKING; WE'RE SINKING; PULL UP.' AT THIS TIME THE CAPT PULLED THE NOSE UP SLOWLY THEN THE GPWS WARNING 'TERRAIN; TERRAIN' AND 'WHOOP-WHOOP PULL UP' SOUNDED. THE CAPT AGGRESSIVELY PULLED THE NOSE UP TO 15-20 DEGS NOSE UP AND FIREWALLED THE THROTTLES. REST OF FLT WAS NORMAL; ALTHOUGH THE 3 OF US WERE PRETTY SHAKEN. LESSONS LEARNED -- PREFLT DISTRACTIONS HAVE TO BE DEALT WITH. PLANNING AHEAD WOULD HAVE PREVENTED THE RADAR FUMBLING; OR TO USE THE AUTOPLT. AND FINALLY; THE FO; OR IN THIS CASE; THE RELIEF PLT IS A VALUABLE ASSET IN MONITORING THE AIRPLANE.