Ok, first...
if (is_file("install.php")) {
Why not use file_exists instead?
$max = rand(0, $count-1);
Basicly, rand sucks.
Use instead...
srand ((double) microtime() * 1000000);
$max = mt_rand(0, $count-1);
$random_quote = mysql_fetch_array($query);
Use mysql_fetch_assoc instead.
$db_name = "$mysql_database";
Why not just?...
$db_name = $mysql_database;
Why name a file .php when there's no PHP code in it (style.php) ?
Escaping so much HTML inside PHP is the most stupid thing ever (it's slow too).