Logout of your primary gmail account.

Login to the secondary gmail account (the one you wanted to add).
Go to https://accounts.google.com/b/0/DisplayUnlockCaptcha and follow the instructions on the page to allow access.

Logout of this account.

Log back into your primary gmail account and now try adding that second account. It should work now.

You should get an email to confirm that you own that account. Make sure you login to that second account again to confirm (by clicking on the link or entering the confirmation code).