MLG FLC HAS EQUIP PROBLEM WITH TRIM CTL. POSSIBLE ALTDEV.

Narrative

UPON DSCNT INTO STEWART FIELD (SWF) PASSING 4000 FT MSL FOR OUR ASSIGNED ALT OF 3500 FT THE GND PROX WARNING SYS GAVE A CONTINUOUS AURAL WARNING (TERRAIN; TERRAIN; ETC). THE ACFT WAS ON THE #2 AUTOPLT SINCE IT WAS THE FO'S LEG TO FLY. AFTER THE 3RD WARNING I DIRECTED THE FO TO INITIATE A CLB WHILE I TALKED TO ATC. WHEN I NOTICED THE ACFT WAS NOT CLBING I INSTRUCTED HIM TO CLB ONCE MORE. AT THAT TIME I NOTICED HE WAS HAVING EXTREME DIFFICULTY PULLING THE NOSE OF THE ACFT UP. I JOINED HIM ON THE CTLS AND MADE SURE THE AUTOPLT WAS DISCONNECTED BY USE OF MY DISCONNECT SWITCH AND THEN VISUALLY NOTICED THE AUTOPLT WAS OFF. AT THAT TIME WE NOTICED THE ACFT WAS TRIMMED FULL NOSE DOWN AND BOTH OUR TRIM SWITCHES WERE INEFFECTIVE. THE MANUAL TRIM WHEEL ALSO WOULD NOT MOVE. DURING THIS TIME I DECLARED AN EMER AND RECEIVED A CLB CLRNC TO 6000 FT WHICH WAS ABOVE THE CLOUD LAYER. WHILE TROUBLESHOOTING THE PROBLEM (APPROX 10-15 MINS) THE TRIM GRADUALLY RETURNED TO NORMAL ON ITS OWN AND WE EXECUTED A NORMAL VISUAL APCH AND LNDG AT KSWF. IT IS POSSIBLE THAT DUE TO OUR INITIAL PROBLEM IN CLBING THE ACFT AND THUS THE DELAY IN CONTACTING ATC THAT AN ALT VIOLATION OCCURRED.