Having a monitor hooked/not hooked to a PC has absolutely no effect on booting.
I'm sure it's still booting into Windows, even though you can't see it. Turn on the PC without the monitor attached, wait a while for windows to load and then try plugging in the montor to see if it has.
Tell me if I understand the real nature of your question...
You have a PC with a monitor and a TV hooked up to it and you use the TV-out to play games.
You want to boot without the monitor connected, using the TV as the primary display.
There are probably hundreds of people in this forum running MAME cabinets with just a TV so I know it's possible.
It may require special video settings, updated drivers, or an external utility.
What video card are you using? This may make a difference.
If you are using a Nvidia based card, check out the TVTool utility...
http://tvtool.info/index_e.htm