How long ago did you set up the accounts on the older computer? Every now and then things change at Gmail and it's possible you have to do something else to get an older account working. I'd go to the Gmail website and see if there are any prompts there to change your password, fill in a captcha or similar. You might need to create a so-called "application-specific password", or confirm that this attempt to connect from a new computer is legitimate. I use OAuth2 and two-factor authentication with my Gmail accounts. This seems to avoid the sort of problem you're having now, but at the expense (in terms of effort) of having to enter into Thunderbird a 6-digit number sent to my phone via sms. This may not be entirely relevant, but in your position I'd have copied the working profile from the old computer to the new, transferring all my settings, address books, extensions, filters and stored messages. However, doing this wouldn't have necessarily fixed your current problem.