Why do you want to have the entire file in an array? In almost all cases it is far better to process your file line by line.
eg.

while (my $line = <$fh>){
    if (#line matches what you're after...){
        # Do action on it here...
    }
}
[download]

When dealing with large files, it is often helpful to 'rewind' your filehandles if you are checking the last couple of lines for something and then need to go back a bit or even back to the very beginning. If thats what you're after, check out tell and seek

Update:
Since Tie::File does not load the entire file into memory, and you are still getting an out of memory error, maybe you can experiment with Tie::File's memory settings.