Drupal 6 Site Duplication - Looks Like My Theme is Broken
/sites/*/files/css/ and /sites/*/files/js should be empty just after migration - do not copy their contend. Clear them.
Before making original site database snapshot, turn off css and js aggregation. If you didn't, turn it off now. If you don't, the duplicated site will be looking for the aggregated content which may, or may not be available on the new site.
On new site, make sure /sites/*/files/ directories are writeable by your php scripts, and that php can delete files too.
Search all theme files for not-relative URIs. There shouldn't be any.
Fix one problem at a time. First, make it work without aggregation (most probably it's URI problem), and only then attempt to fix aggregation issues.
At the end, if you still have problem - disable and then enable theme. This should ensure all theme-related caches are regenerated and theme settings variables refreshed.