A B737-300 EGPWS 'TERRAIN; PULL UP' ALERTED CLBING THROUGH 1000 FT AFTER TKOF. THE CIRCUIT BREAKER WAS PULLED. LATER; ON APCH AT DEST BOTH FMC'S FAILED. FAILURES NOT RELATED.

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ON CLBOUT OF ZZZ AT APPROX 1000 FT AGL; THE GPWS BEGAN TO ALERT TERRAIN PULL UP. WE WERE VFR AND CONTINUED CLB AS THE ALERT CONTINUED TO SOUND REPEATEDLY. I NOTICED THE CAPT'S RADIO ALTIMETER CYCLING. I ADVISED THE FO TO INHIBIT THE GPWS SWITCHES USING CAPT'S EMER AUTH TO SILENCE THE GPWS. AFTER CONFERRING WITH DISPATCH AND MAINT; WE ELECTED TO PULL THE CIRCUIT BREAKER FOR THE CAPT'S RADIO ALTIMETER AND CONTINUE ON TO ZZZ1 WHERE THE WX WAS OVCST BUT BASICALLY VFR. DISPATCH SENT US THE MEL INFO FOR THE #1 RADIO ALTIMETER BEING INOP. AFTER REVIEW; WE FELT THAT WE SHOULD LEAVE THE BREAKER OUT SO WE WOULD NOT ENCOUNTER ANY MORE FALSE GPWS WARNINGS. ON DSCNT OUT OF FL200 BOTH FMC'S FAILED AND ALL WAYPOINTS AND PROGRAMMED ROUTING INFO DISAPPEARED. WE ADVISED ATC THAT WE HAD LOST SOME OF OUR NAV CAPABILITIES AND THAT WE WERE USING RAW DATA. WE WERE VECTORED TO A NON EVENTFUL VISUAL APCH TO ZZZ1 AND EXECUTED A NORMAL LNDG. IF THIS WOULD HAVE BEEN IMC CONDITIONS AT ZZZ; WE WOULD HAVE HAD TO EXECUTE AN ESCAPE MANEUVER. WE WERE ALSO NOT EXPECTING TO LOSE THE FMC'S WHICH ALSO COULD HAVE PROVED INTERESTING IF THE WX WERE WORSE. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING INFO: THE REPORTER STATED THAT THE RADAR ALTIMETER FAILED AFTER TKOF CAUSING THE EGPWS FAILURE. THERE WAS NO APPARENT CONNECTION BETWEEN THE RADAR ALTIMETER FAILURE AND THE FMC FAILURE. SUPPLEMENTAL INFO FROM ACN 809097: I ASKED THE CAPT IF HE WANTED ME TO PLACE THE 'FLAP INHIBITOR' SWITCH TO OFF. HE SAID YES; AND I DID. IT SEEMED TO HAVE NO EFFECT ALTHOUGH WE DID SHORTLY THEREAFTER GET A 'TOO LOW; GEAR' WARNING. ONCE ABOVE FL180 WE GOT IN THE FLT MANUAL. WE FOUND NO CHKLISTS -- JUST SYS INFO. WE THEN WENT TO THE FOM FOR GENERAL INFO. WE THEN REASONED OUR PROB WAS IN THE CAPT'S RADAR ALTIMETER AND FOUND GUIDANCE ON ALL SYS THAT RECEIVE INFO FROM HIS RA. WITH THIS INFO THE CAPT TALKED WITH DISPATCH LISTENING IN WHILE I FLEW THE AIRPLANE AND HANDLED ATC RADIO CALLS. AFTER THE CAPT TALKED WITH DISPATCH; WE TALKED AND DECIDED THE BEST COURSE WAS TO LEAVE THE P-18; B-5 CIRCUIT BREAKERS PULLED AS DIRECTED AND LAND. ON DSCNT; WE LOST BOTH FMC'S; PROCEEDED VIA VECTORS AND A VISUAL APCH.