Can't set up gmail account. Trying to setup leads to dead end in Google Accounts help page about enabling/disabling cookies.

Trying to set up my gmail account. I changed my password because of security issues and was able to make the change painlessly in TBird on my main computer, but won’t allow me to make the change on my other computer. So I deleted the gmail account on my other computer and tried to set it up from scratch assuming this would solve the problem. Same problem. Here’s what happens: while setting up the account I sign in using name, address and new password. Clicked on “Continue”. I noted that the button is set to “imap (remote folders)”. I checked manual config to check the settings: auth set to 0Auth2, SSL set to SSL/TLS. Clicked “Done”. This sent me to the Google Account sign-in page. My email appears, pressed the blue “Next” button, which sends me to another sign-in page. I put in my password again, pressed blue sign-in button, which takes me to a Google Accounts Help page about enabling or disabling cookies (???). There is nowhere to go from there…dead end. Any help would be appreciated.