Four Megabytes isn't a BIG-BIG file, unless you're still using a Commodore-64 computer or a PC-XT. You should be able to loop your way through the file reading line by line, and disposing of the line if it's irrelevant before moving onto the next one, like this:

my( $found, $lineno );
while ( <DATA> ) {
    if ( /keyID/ ) {
        $found = $_;
        $lineno = $.;
        print "Found $found at line $lineno.\n";
        last;
    }
}
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That ought to get through your file in pretty short order, and won't consume copious amounts of memory.