GoDaddy email issues are plentiful, but I have not been able to find anyone resolve this same problem:

I have a GoDaddy hosted site, and a Google Apps account. The MX info on GoDaddy is correct, as is my server-side code, and the Google Apps credentials in my web.config file (host:smtp.gmail.com, port:587) are correct. I know this because I am able to send emails through SmtpClient hosted my local machine's server when debugging the site. However, once transferred to the GoDaddy hosting account, all emails will not send -- they just time out. Nothing has changed aside from the site being run on the GoDaddy server as opposed to a local server.

EDIT - SSL is enabled.

A two part question: 1) Does anybody have any ideas about how to tackle this? 2) If not, is there another web hosting or email hosting site, or a combination of 2, that people can confirm is fast, actually works, and is not impossible to coordinate as is everything with GoDaddy? (I am aware that GoDaddy has their own relaying email server, but I initially used it before switching to Google and found emails coming in 30-60 minutes late).