is there a way to connect the composite video cable to the gpio connectors? like one end of the cable in the tv and the other connected to the gpio?
what do you think that would accomplish? No the GPIO's cannot create a video signals.
I'm still guessing you have not managed to set up the system so that it actually boots (without the HDMI connector connected, could be a missing ground issue, yes its theoretically possible that the PI doesn't receive power when you pull the HDMI plug, as the HDMI cable might close a otherwise missing ground loop. its very
The PI has no BIOS, so it won't actually create any
video signal until it manages to boot from a well crafted SD-card.
The only way, (without a video signal) you can tell if the PI at least attempts to boot is by observing the green LED.
by the way, why, if the PI can generate a HDMI signal, do you still need it to generate the far worse composite video?
Do you understand the use of config.txt? It can be changed to boot Raspbian with a range of different Composite signals, but default is NTSC, which your TV might not like.
In contrast simply booting NOOBS will never
generate a composite signal, not even with a pulled HDMI cable, unless you command it to do so by pressing the right key on an attached and working keyboard ('3' or '4').
So you should be able to boot NOOBS with both HDMI and composite cables connected, and by pressing the keys 1 to 4 you should be able to switch "live" from HDMI-optimal or HDMI-safe to PAL or NTSC, and back.