It's not really necessary to re-write everything. You only really need to change things that require functions that are depreciated in PHP 5 or where there is a newer technique or driver e.g. Database access.
Have you uploaded the image to the server too and is it in the correct directory? If that's not the problem, can you provide a link to the page in question.
For what it's worth, storing PHP in a database for execution is a hideously bad way of getting around a problem. In no case should you ever have to do it.
I must say, your site looks very professional and clean. Besides the issues with the login bar overlapping the title, I am having a hard time finding anything that needs changing.
Resource usage suspensions are not based upon bandwidth, they are based upon CPU usage of your scripts. This is usually because people have too many plugins installed on their sites.
mod_rewrite is enabled on all free servers.
You will not, however, have access to the httpd.conf file on a free server, you would need to purchase a VPS to do so.
It now looks considerably better than it did to start with. The only major thing I would recommend to change would be the banner, as others have said.
The background gradient isn't too bad, it may need a bit of tweaking though.