Our standard View Cart code includes a section of javascript that manages the overlay-style cart display "inside" your page, so if that code is missing or removed from a page, the remaining buttons on that page would operate in "fallback" mode by displaying the cart in a popup window/tab.
"This product combination does not exist" would appear if your product is using Variants and the buyer selects a combination of Variant options that isn't defined in that product's Define Variants screen. This can also happen if you change the product's Item Number in Seller Admin after you have already pasted the button code into your page, so the Item Number referenced in that button code no longer matches the Item Number of any product in your Seller Admin.
Looking at your page, I was able to isolate the problem to this section of code, where the <option> tags are missing value= attributes:
<p><select name="o2" class="first product-attr-delivery delivery"><option>USPS</option><option>Pick-up</option><option>Delivery</option></select> <input type="hidden" name="on1" value="Date"/><input name="os1" class="second product-attr-date pickup invis" type="text" name="os1" /></p>
Apparently most browsers treat the content of an OPTION element as its value if no value= attribute is specified in the opening <option> tag, but IE doesn't do this. Compare to the standard button code provided in your Seller Admin for that option:
<select name="o2">
<option value="USPS">USPS</option>
<option value="Pick-up">Pick-up</option>
<option value="Delivery">Delivery</option>
</select>