You want to look for transitions from quietParts being true to it being false in order to locate the beginning of non-quiet, and you want to look for transitions from quietParts being false to it being true in order to locate the ending of non-quiet.
A trick involved is to use
quiet_row = quietParts(:).'; %need it as row vector
A = strfind(quiet_row, [1 0]); %silence ends
B = strfind(quiet_row, [0 1]); %silence starts
You need to work out the boundary conditions to figure out whether to use those indices exactly as-is or one before or one after.
Also, you need to be concerned about whether the file begins in silence or not, and whether it ends in silence or not. For that purpose it can be useful to pad quiet_row with false or true on both sides (I leave it to you to work out which is appropriate.)
