In template_contact.php remove line 87 to 103.
<fieldset><?php if (!isset($errorC) || $errorC == true){ ?><h3><span><?php _e('Send us mail','habitat'); ?></span></h3>
<p class="<?php if (isset($the_nameclass)) echo $the_nameclass; ?>" ><input name="yourname" class="text_input is_empty" type="text" id="name" size="20" value='<?php if (isset($the_name)) echo $the_name?>'/><label for="name"><?php _e('Your Name','habitat'); ?>*</label>
</p>
<p class="<?php if (isset($the_emailclass)) echo $the_emailclass; ?>" ><input name="email" class="text_input is_email" type="text" id="email" size="20" value='<?php if (isset($the_email)) echo $the_email ?>' /><label for="email"><?php _e('E-Mail','habitat'); ?>*</label></p>
<p><input name="website" class="text_input" type="text" id="website" size="20" value="<?php if (isset($the_website)) echo $the_website?>"/><label for="website"><?php _e('Website','habitat'); ?></label></p>
<label for="message" class="blocklabel"><?php _e('Your Message','habitat'); ?>*</label>
<p class="<?php if (isset($the_messageclass)) echo $the_messageclass; ?>"><textarea name="message" class="text_area is_empty" cols="40" rows="7" id="message" ><?php if (isset($the_message)) echo $the_message ?></textarea>
<input name="username" value="" id="username" class="username"/>
</p>
<p>
<input type="hidden" id="myemail" name="myemail" value="<?php echo $email_adress_reciever; ?>" />
<input type="hidden" id="myblogname" name="myblogname" value='<?php echo $name_of_your_site; ?>' />
This will remove your standard form. It will not be linked to your custom form as I do not have the time to go and create custom solutions.