See Scott's reply above. I'd be very curious to find out where you're getting your information that most of the ships in Pearl were there because they were broken?
Some years ago a came across a listing of the statuses of the DDs at Pearl Harbor before the strike, but cannot find it now. The after action reports however give some information:
www.history.navy.mil
And based on them:
USS Allen Ready
USS Aylwin Ready
USS Bagley was moored at the Navy Yard Pearl Harbor, T.H., (Berth B22) for restricted availability (repairs to starboard bilge keel)
USS Blue Ready
USS Case undergoing regular scheduled overhaul
USS Cassin Drydock
USS Chew Ready
USS Conyngham The ship was undergoing routine tender overhaul with all main engines, boilers and generators disabled
USS Cummings Restricted availability status undergoing preliminary radar installation work (got underway 10:26)
USS Dale Initially OK, but developed engine problems during the day and needed tender to do the repairs
USS Dewey Under tender overhaul
USS Downes Drydock
USS Farragut Ready
USS Helm Ready
USS Henley Ready
USS Hull Undergoing tender overhaul
USS Jarvis Restricted availability status, got underway 10:18
USS MacDonough Undergoing scheduled overhaul
USS Monaghan Ready
USS Mugford Ready
USS Patterson Ready
USS Phelps Some overhaul work being done, got underway 09:26
USS Ralph Talbot Ready
USS Reid Undergoing repairs, got underway 10:10
USS Selfridge Ready
USS Shaw Drydock
USS Tucker Ready
USS Ward Ready
USS Worden undergoing routine upkeep, got underway 10:40
I count 14 that did not mention any handicaps regarding their readiness, but not sure if that is the full truth. Of course in emergency you may cut any minor overhaul short as was done with many of the ships.
But then again even during an emergency there is a need to maintain anti-submarine patrols at the harbor entrance.