Warming CPU means your CPU is probably getting clock frequency so it may try to start up but fails to tell you what is wrong. Some computers try to communicate through speaker but some just hang.
When I have had similar issues I used diagnostic card (POST Tester). That device can tell where the system hangs (POST code). Some cards also have voltage level indicators. That device offers extra human readable output what is happening inside your computer.
Please note that POST tester is good for problem solving at the boot early stage but it is useless after bios finish its job and OS take command. But usually you should have picture on your screen when that happens.
Those cards don't cost much. From ebay you can find those at the price between 1$ and 10$.