On second thought...

This solution fails if there is a stop-line not balanced by a start-line. A better solution (or at least one that doesn't have a subtle potential bug) is:

use warnings;
use strict;


my $START = qr{ \A Info  [ ] I  [ ] Want                 }xms;
my $STOP  = qr{ \A Start [ ] of [ ] Info [ ] I [ ] don't }xms;


while (<DATA>) {

    # if (/$START/ .. /$STOP/ xor /$STOP/) {
    #     print;
    #     }

    if (/$START/ .. /$STOP/ and not /$STOP/) {
        print;
        }

    }

__DATA__
asdfsdfds
asdfasdf
blah blah blah

Info I Want

I want this line
And this line
And this line

this is the last line i want
Start of Info I don't want

blah blah
blah blah blah

Start of Info I don't want

blah blah
blah blah blah
[download]

<p Output: <p

Info I Want

I want this line
And this line
And this line

this is the last line i want
[download]