As far as I understand your question, you are trying to login to your SQL instance with an account from a separate domain. As your SQL instance won't have permission to see the new domain and therefore check the credentials of the new user it won't allow you to access it.
The server that the instance is hosted on needs to be on the same domain as the user you are trying to log in with. An option would be to add the server to the new domain (which would remove it off the old domain) or use mixed mode authentication and use a SQL login (which isn't best practice).
Hope that helps.
My situation is here. I installed SQLServer on my local computer, while installing I used a domain account T\dtdung for security section which I also used to login into my computer. After that, this account was changed within new domain T_new. Now, my account to login the computer is T_new\dtdung.
I agree with you that the new account does not have sysadmin role. I will try to fix it