Hi, thank you for contacting JustAnswer.com. My name is Russell. I will do my best to provide the right answer to your question.
I would advise you first of all, to clear all Temporary Internet Files, and all Temporary Files, by using Disk Cleanup (if your new computer is a Windows computer.)
Also, run Windows Update on your computer, and make sure your new computer is fully updated, then restart your new computer, and be patient as any new updates installed may make the restart quite slow for a time.
Then try again. And if it does work, please rate my Answer.
If it doesn't work, note the exact error appearing on your screen when the login to WordPress site fails, and let me know by Reply To Expert, what that error message was, please. Thanks.