Several things:
The crash is probably that ADE has somehow got corrupted, or that some OS update has stirred a bug in it.
Even if the book you downloaded is corrupt it wouldn't crash a properly written program: on the other hand, it might well crash ADE.
For non-DRM books (such as Project Gutenberg) I suggest the use of the free Calibre. http://calibre-ebook.com/
Much better than ADE in almost every way ~ only downside I know is it can't handle DRM.
Maybe if you have lots of DRM books and just a couple of free ones it might be worth using ADE for all for consistency.
All your books should be on your PC and unchanged by whatever happened.
They will be readable on any ADE or device that is registered with your Adobe ID (non-DRM ones will be readable on any device).
Always worth backing up any, bought ones esepcially but free ones too just for convenience if you have a crash and lose your main disk.
Your books are NOT held anywhere in the cloud just available for reuse when you move to another computer or move things around on an existing one.
If you uninstall and reinstall ADE you may also need then to deregister (ctrl-shift-D, cmd-shift-D on Mac) and reregister the new copy with your Adobe ID.
When reinstalling ADE I recommend reinstalling the older V1.7.2 as it has many fewer bugs than the recent v2.0/2.0.1.
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There are lots of bugs in ADE2.0 (and 2.0.1). Try replacing ADE2.0 with the older but more reliable v1.7.2.
(You can have them both installed at once if you like.)
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
Some people have found ADE trying to upgrade automatically.
It appears (not 100% sure) that if you install ADE2.0 as a new install (not as an upgrade) that your 1.7.2 will continue to run.
Probably best to say no if 2.0.x installation asks if you want to migrate your library.