The problem is for the dozens and dozens of jobs I apply to online, I've heard back from one... and that was back in March.
FYI... online job applications are mainly resource-stacking on the part of the employer. Your application is likely screened electronically, and if not turfed it is then dumped in to a big ol' bit bucket along with a few hundred other electronic applications. In most cases your application becomes a needle in a haystack.
You'll have a much better chance of getting noticed if you find a warm body to use as your "in".