The biggest problem I can see is the original v4 license was probably never deactivated on the original machine/installation. And even after all this time any attempt to use the same license for another installation simply looks like someone trying to install a second instance of the software -- which is then prohibited by the database that keeps track of all that stuff because it thinks the original installation is still active as well.
Seems to historically be a frequent problem that would obviously receive greater attention for currently (or recently) licensed users. May not seem fair, but also doesn't seem like there's another way to deal with it given the limited support available for so many current users who are indeed paying for an initial or updated support license. Just the way it is.
Perhaps a new support request with a subject like "Deactivation Request of License Key xxxxxxxxxxxxx to Move Current Installation to New Machine" will receive more attention than the last try? The license key would automatically be included in the subject for reference if using BI itself to generate the request. I would recommend including it in the subject of any new correspondence as well. Gives em something to go on to prioritize responses according to whatever protocol they have in place.