C4 engine look good

Do you have to display their logo on engine start up or any where else in your game.
Yes.
This is easy to find at their website:
http://www.terathon.com/c4engine/stdlicense.php2. For each Work created by the Licensee using the C4 Engine and distributed by any means, the “Powered by the C4 Engine” logo provided by the Licensor must be displayed as follows.
(a) If the Work has a title screen, then the logo must appear on the title screen. Alternatively, the Work may display the logo by itself for not less than one second before the title screen appears each time the Work is launched. In either case, the logo must be displayed at a reasonable size not less than 256 pixels in width.
(b) If the Work is distributed in a physical package, then the logo must be printed on the package at a size not less than one inch (2.54 cm) in width.
(c) In no case shall the logo be cropped or modified in appearance from its original form.