Assuming that from a non booting DELL Dimension 4400 the P4,1.6,478 Socket,266FSB CPU ist still OK,what would be a Motherboard that would fit this CPU in an other ATX Case?

see what you can find: http://shop.store.yahoo.com/justdeals/so478pe4mo.html

I found a MB with a TRIOPTIX Form Factor. Is this the same as ATX?

Dells don't use ATX, they use micro-ATX just get a microATX socket478 mobo and put it in the Dell case, which will be alot easier then putting everything in a new case. It says not to put a question here... why not?

Have you tried your power supply in another computer, or tried another power supply in your computer? If you haven't, a failed power supply is one of the most common reasons a mboard won't boot. I checked out whether your power supply has proprietary wiring here: http://www.power-on.com/atx250dl.html - it doesn't - the Main connector is standard ATX - any standard ATX PS of 250watts or more will do, as long as it has the needed connectors. If the main connector colors of the wires on the other PS are the same, it is also standard ATX.