Got it working! I compared the working code on the original signup page (news.php) and realized the input name "subscribe_lng" and id "semail" were different. It may not be perfect but it works!
This is the code I used to get the newsletter signup on the front page of our store without verification image check:
Code:
<form name="subscribeform" action="news.php" method="post">
<input type="hidden" name="subscribe_lng" value="en">
<input type="hidden" name="s_lists[]" value="1">
<input type="hidden" name="skip_validation" value="Y">
<input type="text" name="newsemail" size="30" id="semail" value="">
<input type="hidden" name="sl" value="en">
<button class="button main-button" type="submit" title="Subscribe">
<span class="button-right"><span class="button-left">Subscribe</span></span>
</button>
</form>
Also make sure you disable image verification on the modules section for newsletters.
Thanks Alex for you help!