Help! I am having the same problem as well. I had ADE 3.0 installed & it was still working properly about 3 weeks ago. When I tried to open a book I had downloaded from our library yesterday, I got the connection error, cant connect to the fulfillment server, make sure you are connected to the internet. I have tried uninstalling 3.0, reinstalling it, uninstalling & updating to 4.0.3, and I am still getting the same error message. I can open a sample book I downloaded from from Adobe, but books from my library won't transfer & open. I have also tried to deauthorize my computer so I can reauthorize it & I get a check internet connection message.
Try running ADE from your admin account on your computer. That ended up working for me. I tried all the fixes on here, did the control shift d to deauthorize & then couldn't authorize again, got can't connect to the activation server. When I went into it from my admin account & had to click on help, deauthrorize & then authorize. I could then add the borrowed library book & transfer it to my Kobo Glo.