The only alternative to ADE I know for working with Adobe DRM books on PC/Mac is Sony Reader.
Free download from Sony intended to run with Sony eReaders but works quite happily without.
https://ebookstore.sony.com/download/
You may have more luck with that.
Unfortunately, it is still subject to some of the quirks of the Adobe registration/authorization mechanism.
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The ADE launching problem looks as if it is an issue either with your browser, or with Windows itself.
Or maybe your download manager if you have one installed.
Most browsers/managers will put the download on you computer anyway, and then launch the file if it can.
All that assuming you are using a standard browser to access the online library: is that correct?
