You have just learned why this is the "wrong" way to do it

To put the function override into your theme, copy the "theme_" function into template.php (Found in your theme directory. If it's not there just create it - some themes don't have a version of this file). Edit template.php and change the "theme_" in the function name to be "yourthemename_", where "yourthemename" is the actual name of your theme, or you can use "phptemplate_" instead. Then modify the code in the function to emit the HTML you want.