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It may help (no promise) to completely deauthorize first: it sometimes gets into a half and half state.
In ADE Library view, hit ctrl-shift-D (cmd-shift-D on a Mac).
Restart ADE.
Try again to authorize.
~~~
Try with your antivirus and firewall temporarily turned off.
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Another thing that may help is to install the older but more reliable ADE1.7.2 and try registering that.
Version 1.7.2, it is a little difficult to find, available on Adobe site for Windows and for Mac.
http://helpx.adobe.com/digital-editions/kb/cant-install-digital-editio ns.html
The forum software is sometimes corrupting the link above. There shouldn't be a blank in 'editio ns.html'. The following redirects to the same page: http://tinyurl.com/diged172