I think you are simply skipping quotes around "hidden_div" in your call to document.getElementById("hidden_div") !
But in fact, your page is probably sent back, resetting the page state and leaving hidden_div seemingly always in a hidden state - are you going to handle submitting the form via AJAX?
If you want to see the intended behavior, you must move the showHide() call to the <form> element and return it after it:
<form method="post" name="installer" onsubmit="showHide(); return false;">
and leave the submit button as:
<input type="submit" value="" name="submit" />
Also note that you did not close the <input /> button tag or did not receive any text displayed inside it.
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