I had this error and was able to resolve it. My case might be unique but I thought I'd share in case it helps anyone:
I was getting the "You cannot sign in at the moment. This is likely caused by a bad internet connection" error only when using wifi at home, with AT&T.
If I use the internet at work (Comcast), a VPN, or tether to my phone on data, it works fine. If I tether to my phone while the phone is connected to my wifi at home, it doesn't work and I get the error.
I think for me, AT&T arbitrarily blocks certain IP addresses (I've had similar issues with other websites. for example, on my AT&T internet at home, www.giftcardmall.com works fine but the mygift.giftcardmall.com subdomain is blocked, but on mobile data or on other people's internet, it works fine. I've tested turning off the firewall on my modem at home and it still doesn't change anything, and obviously AT&T customer support doesn't care.)
Again, not sure if this helps anyone else, but if you have the same issue I do with mygift.giftcardmall.com, maybe it's an issue of your ISP rather than Evernote?
