Here's my opinion:
Most recent systems (BIOS) can't boot without a video card (you might have an option in the BIOS enabling it). Thus resulting in the PC shutting down. It's probably restarting because it keeps trying to find your video card...
To my knowledge, you should be hearing a beeping sound each time it restarts. If you do, google '
bios beep codes'. You'll know exactly what's your problem (probably missing video card... which is normal in your case!).
It's also normal the fans are spinning fast/loud when you boot.
I wouldn't be worried, but then again, I could be wrong.
Hope this helps, even though it wasn't much