Windows にはstrptimeが存在しないようなので、特定の形式だけサポート。 手抜きなので、注意。
#include <stdio.h>
#include <time.h>

static
time_t
get_t_time_from_string(char *timebuf)
{
  int res;
  int year, month, day, hour, minute, second = 0;
  char wday[36];
  struct tm tm;

  if (strlen(timebuf)>36) {
     return 0;
  }

  /* old version */
  res = sscanf(timebuf, "%d/%d/%d %d:%d", 
        &year, &month, &day, 
               &hour, &minute);
  
  /* format error */
  if (res < 1) {
     return 0;
  }

  if (year > 1999) {
     res = sscanf(timebuf, "%d/%d/%d%s %d:%d:%d", 
         &year, &month, &day, 
                  wday, &hour, &minute, &second);
     if (res < 7) {
        return 0;
     }
  }
  else {
     if (res < 5) {
        return 0;
     }
     year = year + 2000;
  }

  tm.tm_sec = second;
  tm.tm_min = minute;
  tm.tm_hour = hour;
  tm.tm_mday = day;
  tm.tm_mon = month - 1;
  tm.tm_year = year - 1900;
  tm.tm_isdst = -1;

  return mktime(&tm);
}

int
main(int argc, char **argv)
{
  time_t t1;
  time_t t2;
  struct tm *tm1;
  struct tm *tm2;
  char buf1[256];
  char buf2[256];

  t1 = get_t_time_from_string("02/03/13 22:59");
  t2 = get_t_time_from_string("2006/08/05(土) 06:40:09");

  printf("t1=%d\n", t1);
  printf("t2=%d\n", t2);

  tm1 = localtime(&t1);
  
  strftime(buf1, sizeof(buf1),
    "%a %Y-%m-%d %H:%M:%S %Z", tm1);
  printf("%s\n", buf1);

  tm2 = localtime(&t2);

  strftime(buf2, sizeof(buf2), 
    "%a %Y-%m-%d %H:%M:%S %Z", tm2);
  printf("%s\n", buf2);
  return 0;
}