If Windows Explorer was used to copy the coverages from one computer to another, or otherwise move them around, the coverages can fail because the associated INFO folder isn't present or properly updated. ArcCatalog should be used to move the coverages, or the coverages should be converted to e00 files, then moved (by Windows Explorer or ArcCatalog), then imported back to coverages. So you might use ArcCatalog to delete the coverages on the machine where they are failing, and then use it again to copy the coverages on the computer that are functioning properly or to create the e00s to move over to where they failed.
One complication. Sometimes even ArcCatalog doesn't get rid of an INFO table properly so if copying the coverage fails you might look for a table that has the same name in ArcCatalog, perhaps with an xcode extension, and delete that, refresh ArcCatalog and then try to copy.