There is likely two problems here:

1. The captcha is probably not working due to a lack of GD libraries being installed on your VPS. I would have Godaddy ensure that they are in fact installed.

2. With regards to the email, this may be due to Gmail. Google's spam system treats a lot of large hosting provider's IPs are potential spam and may have inadvertently sent your signup email to your SPAM folder (or, it could have dropped the connection all together. I would first check your spam folder. If it isn't there, you can do a check at mxtoolbox.com (enter your server's IP) and see if it's blacklisted anywhere.