If the RadComboBox displays properly after removing your custom CSS, this means that the CSS is interfering with the built-in CSS of the control.
When only using the built-in CSS, the 'select' text is rendered however it is not visible as an Image displays on its place.
Could you provide more details about what you are trying to achieve with the custom CSS (change the arrow image, font, borders attributes, etc.)? Additionally, pasting here the CSS code could help us in identifying which rule exactly breaks the display.
the Telerik team