Hello,
But you probably do not use system template. Do you have that file in template you are using? And does exist template.css in your default template?
Only thing component.php needs is to load main css file with styles for fieldsets, h1, tables etc. Then it will design that popup with those styles. When I remove component.php from Joomla template beez_20, I get same problem as you get. My default template is that beez_20 and Joomla will not use component.php from system.
You can try to test it with another template what was implemented in Joomla installation. Is there same problem? Those templates should work in this case, because they are made with Joomla standards, where every template should contain component.php file.
EDIT: If you have troubles to set it, we can also help you as paid custom support, because we don't think this is bug of our component. It can be clear and fast. If you are interesting in, let us know on
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But first, you can try those tests with Joomla templates.