Make sure your tv comes on from a power loss. What you need to do to test this is plug your tv into a power strip with it on.
Flip the power strip off. Then turn it back on and see if the tv comes back on. If so. You are in luck.
You will also want the input mode to come on as well. Set the TV to input 1 or 2 and run the same test. If the tv turns on and is showing input 1 then this tv is perfect for the arcade machine. If it turns on and goes to TV you will have to switch it to input 1 manually or with the remote. You can take the tv apart and work around having to do this.
Next you build a relay controled power strip that works off the 12 volts of your pc. I followed the below instruction as an example only and used a power strip instead of a home outlet. Works like a charm. I turn my pc on and it turns on the speakers, fan, monitor(or TV) all at once. Very professional.