Try this,
1. Type your email address into Settings > General > Email Address
2. The contact form on my site works fine. Copy and paste this into your site:
<div class="contact-area">
<form class="contact-form" method="post" action="">
<input type="text" name="name" id="name" value="" placeholder="NAME" size="22" tabindex="1" aria-required="true">
<input type="text" name="email" id="email" value="" placeholder="EMAIL" size="22" tabindex="2" aria-required="true">
<textarea name="message" id="message" cols="39" rows="7" tabindex="4" placeholder="Message"></textarea>
<p class="noticefailed"></p>
<input type="hidden" name="sendto" id="sendto" value="(Default Admin Email)">
<input type="button" name="submit" id="submit" value="SEND">
</form></div>
3. Type a message into the form and click send.
4. Check your email to see if it's there.