It is just a question of organizing the facts to test in a convenient way that can be tested without too much muss or fuss. The following untested validation function should do it:

# Tests the start_hour, start_minute, end_hour, and end_minute
# pulldowns to verify that a consistent set of them have been
# specified, and that the start time (if specified) is before
# the end time.
sub validate_date_pulldowns {
  if (defined(param('end_hour'))) {
    return 0 unless defined(param('start_hour'));
    return 0 if param('start_hour') > param('end_hour');
  }
  if (defined(param('start_minute'))) {
    return 0 unless defined(param('start_hour'));
  }
  if (defined(param('end_minute'))) {
    return 0 unless defined(param('start_minute'));
    return 0 unless defined(param('end_hour'));
    return 0
      if param('start_hour') == param('end_hour') and
         param('start_minute') > param('end_minute');
  }
  return 1;
}
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It would be easy to extend this code sample to add in support for start/end seconds as well.

Update: Note that the key idea is my strategy of turning many combinations of conditions into a set of "guard conditions" on which you exit early. I've found that this strategy often converts deep nested decision trees into a series of fairly straightforward decisions (as above).