Hi there,
since you don't have a control over the server there's nothing you can do to in order to make the default mail() function work.
To be really really sure create a file with just one line:
mail('your@address.com', 'this is a test', 'test body');
I have been sure so many times and yet I was proven wrong later. So it's best to make your tests as simple as possible.
If you get the test message when run on your dev box but not from the production server you should give this script to the hosting company and tell them to fix their setup.
If they tell you to screw yourself you'll have to work around it. Consider using some mail() replacement like the excellent XPertMailer:
http://xpertmailer.sourceforge.net/
You can switch it to use a direct SMTP connection instead of default mail() function. For that case you will need to know what's your hosting's SMTP server for outgoing connections. Or you will have to use some other SMTP server, likely with SMTP authentication turned on.
XPertMailer has one additional feature and that is to connect to SMTP server of the recipient domain. That way the e-mail is sent through different SMTP servers, no need to use your own SMTP server.
Petr