I think you are right. I checked again with the Evernote account info and it only shows 1 device linked, it does not count browser.
I tried to log in with email on mobile and use wifi -> the same issue happened.
I tried to log in with email on mobile and use mobile network -> I was able to log in with email, the password textfiled showed up. Great!
So, i think there is an issue with my wifi. However, I tried with LAN network at work/my office, the same issue happened, I could not log in with my email. I use my email to log in instead of via Google account since I could not use gmail at work, my company blocks some Google services.
I guess the only option I have now is logging in via email with mobile network. I suppose it is a temporary solution at this moment.
Thank you guys so much for helping me, @PinkElephant and @agsteele. Have a nice weekend!!!