Early 2011 Macbook Pro boots, then shuts off
I too had a battery-less MBP early 2011. The full speed fan effect is normal in this case, AFAIK. Seems to be by design.
It's only when I installed a battery, even if it was faulty (third party) that I could do something on the machine.
I would advise you not to loose any more time and order/borrow a battery.