awk -v From="03/Jan/2008" -v To="24/Jul/2008" '
function cnvDate(date   ,d) {
   split(tolower(date), d, "/");
   return sprintf("%04.4d%02.2d%02.2d", d[3], month[d[2]], d[1]);
}
BEGIN {
   FS = "[:[]";
   month["jan"]=1 ; month["feb"]=2 ; month["mar"]=3 ; month["apr"]=4 ;
   month["may"]=5 ; month["jun"]=6 ; month["jul"]=7 ; month["aug"]=8 ;
   month["sep"]=9 ; month["oct"]=10; month["nov"]=11; month["dec"]=12;
   date_from = cnvDate(From);
   date_to   = cnvDate(To);
}
{
   date = cnvDate($2)
   if (date >= date_from && date <= date_to)
      print;
}
' inputfile