Post from above (from Arbie)...This is what I use and have never had issues getting it to work:
There are two separate things here.
The first is that if there is not a shared or dedicated SSL that you can use on your server it wont matter what you do as you will not be able to use https
The second is that there is a problem for you using the php code in your site which is usually caused by whitespace in a php file somewhere. No matter - there is another way.
What you need to do is go to your .htaccess file on your server (if there is not one then create one).
Add this to the very start of the file.
RewriteEngine On
RewriteCond %{SERVER_PORT} 80
RewriteCond %{REQUEST_URI} the_page_to_use_https/
RewriteRule ^(.*)$ https://mysite.com/the_page_to_use_https [R,L]
This wont get upset by any php whitespace and should solve your issue provided there is an SSL cert you can use.
https for wordpress will then help to tidy up the secured page by attempting to make sure that all of the media links on the page are https calls rather than http, so preventing the irritating mixed content message in IE
Finally, godaddy have dedicated SSL certs at $15 so there is no excuse not to protect your customers!
https://www.godaddy.com/gdshop/ssl/ssl.asp?ci=8979
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