Exactly where is it happening.
Most likely is that you have changed your authorization, and a book authorized under the old ID can no longer be read.
It is true what you said I did not have an ID then after I singed up for ID to use my ebook in more than one unit. So what can I do to get back the book now
there was not an old ID I did not use the book with and ID firstly. So still need to know how to get back my book
If you originally loaded the book when you were running ADE without ID, and have now registered an ID, you are probably stuck.
This is a vicious trap that Adobe lays for unsuspecting customers.
When you register 'without ID', ADE creates an anonymous/implicit ID with limited powers (eg can't be used to share with other devices).
Whenever you first load a DRM book, that copy of the book is associated with whatever ID the computer is registered to at the time.
Any book you load while this anonymous ID is active gets associated with that ID, and can't be read on any other device.
When you properly register your computer with a real ID, that old anonymous ID is lost.
Now you don't have any devices that can read the book.