Mate of mine did a Daytona racing setup using two laptops, without batteries, and got them to startup automatically by using capacitors across the power button terminals.
To turn off, just cut the power. If using Linux-based OS and mostly just playing games (reading data), this should be fine.
No doubt there was some hacking. Unfortunately there was no writeup so I forget if there was anything else notable involved - we were just chatting and sharing photos.
The cap simulates a button press & release. Cap takes a small while to charge = switch circuit is closed (presses). Once cap is charged = switch open (released).
Larger caps take longer to charge, therefore longer delay before release. Start with electrolytic, say 10uf or 100uf cap. Cap goes on DC logic part of the switch, not any parts connected to AC power. Make sure the positive lead goes to the active, negative lead to earth.
He stole the idea from me - I use the "cap trick" sometimes to get stubborn TVs to turn on automatically. But then, I stole it from someone else a long time ago, so all's fair.