I just took a look at your site and GD is not installed on it so that is going to be the problem dealing with the captcha.

As for the emails, I also did a quick check and see that your VPS is running CPanel 11. Another quick check showed that SMTP (port 25) on your server is closed. This would suggest that your server is running CSF (ConfigServer Security & Firewall). CSF is generally included with CPanel 11 and is a bi-directional firewall (meaning that it can block both incoming and outgoing connections). If port 25, which is normally open on a Cpanel server (so that you can receive email) is closed inbound, it is also likely that port 25 is closed outbound as well (sending email). You may want to have your server people also check to make sure that port 25 is open in both directions on your server.