When the infamous phrase "you only have one attempt left" appears I'm thinking I'll try the recovery procedure and typed in my mnemonic.
Password guesses are not limited so this sounds like a problem with 2 factor authentication to me. Do you have two factor authentication enabled? If so please use the form at
https://blockchain.info/wallet/reset-two-factor in order to have it removed after which you will be able to login using only the password.
If 2fA is the problem, you might wanna simply check you don't have NoScript addon or an equivalent running, too, and if that's the case, either whitelist blockchain or temporary authorize it before trying to login.