One way is to use Range Operators:

use warnings;
use strict;

while (<DATA>) {
    print if (/start/i .. /end/i)
}

__DATA__
foo
start
checking
script
end 
foo
[download]

And to exclude the start/end:

    if (/start/i .. /end/i) {
        print unless /start/i or /end/i;
    }
[download]