No. All ports closed? You are in the same position as this guy.
Unfortunately, you have no options to use Gmail with your current host, other than begging them to open the ports. The only option you have for sending mail at all is doing it through your host's SMTP server using an e-mail address that they allow.
Google will simply not accept mail relayed through an external server for one of their own users. i.e. if you address an email as coming FROM your gmail address, you can never send it TO someone with a gmail address.
Sorry :-/