If the Ids are unique this is of course a good solution, but if not this has a caveat... if there happen to be two Success sections with the same Id right after each other, the second one won't be matched unless the second regex is changed accordingly:

use warnings;
use strict;

my $ID = '5678';

while (<DATA>) {
    my $match = /^Success.*Id-\Q$ID\E/i
        ... /^Success.*Id-(?!\Q$ID\E)/i;
    print if $match && $match !~ /E/;
}

__DATA__
One
Success|Id-abcd
Two
Success|Id-1234
Three
Success|Id-abcd
Four
Success|Id-5678
Five
Success|Id-5678
Six
Success|Id-9900
Seven
Success|Id-5678
Eight
Success|Id-0000
Nine
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