Out of curiosity, have you tried opening them in calibre's editor and run at least it's built-in checker? Preferably you would also add the epubcheck plugin for the editor and use that as well. Garbage in, garbage out definitely applies to ebook conversions.
However from your comments, I would tend to suspect that you are attempting to convert a fixed layout epub to mobi which is not going to work. Again, using calibre's editor to open the epub and check in the content.opf (found it under the Miscellaneous heading) to see if it has lines such as:
<meta property="rendition:layout">pre-paginated</meta>
or
<meta name="fixed-layout" content="true"/>
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