I would see what module positions are available on your template. You can do this by adding tp=1 to the query string like so:
http://www.joomla.org/index.php?tp=1If you have a template position where you want your static HTML, just create a custom HTML module and put your static HTML in there.
If you don't have a module position, you can add one by editing your template's index.php file here:
.../templates/YOURTEMPLATE/index.phpAnother option would be to just hard code your static HTML into your template by editing your template's index.php.
Let me know if I misunderstood.