when i view source of the cart page, the delete checkbox does not have a value:
<td class="eC_FormItem" ><input type="checkbox" value="" name="eCart1_Delete_0" /></td>
it should be getting a value from the cart ID column:
<td class="eC_FormItem" ><input type="checkbox" value="<?php echo $eCart1->DisplayInfo("ID"); ?>" name="eCart1_Delete_<?php echo $eCart1->DisplayIndex; ?>" /></td>
double check in the add to cart buttons that you are giving the ID cart column a value.