/^Request Number:/
/^Status:/
/^Affected User:/
...
/\d+\s+minutes\s+\d+\s+seconds/  # (update: had forgotten 3rd "\s+")

##</code><code>##

my %record;
if ( /^Request Number:/ ) {
   my @flds = ();
   push @flds, substring( $_, 0, 40 );
   push @flds, substring( $_, 40, 26 );
   push @flds, substring( $_, 66 );  # rest of line
   for my $fldname ('Request Number', 'Parent', 'Priority') {
      (my $val = shift @flds) =~ s/^$fldname\s*:\s*//;
      $val =~ s/\s*$//;          # update: remove leading/trailing whitespace...
      $record{$fldname} = $val;  # which means this could be "" -- not a problem
   }
}
# and likewise for each other type of line

##</code><code>##

$/ = "end-of-record-string"; # whatever that may be

while (<>) {  # this now reads one whole record into $_
   my @lines = split( /\n/ );
   my %record
   while ( @lines ) {
      $_ = shift @lines;
      # proceed with parsing record fields as above...
      if ( /^Request Number:/ ) {
        ...
      }
      elsif ...
   }
   store_to_database( \%record );
}