The only wires you need worry about are the heavy cable coming down from the battery. If it touches the frame you get fireworks. Maybe even blow the battery, melt some wires.
And the red/white wire, It's hot when you turn the key on and stays hot till the engine starts. This is power to the starter relay. The blue/white as mentioned goes to the start button where when pushed the button grounds the b/w wire. This completes the circuit and trips the starter relay and connects the large cable from the battery to large cable to the starter.
Now looking at your pic there is a wire bundle with a red wire that has a woven cover. This is the main power wire to the main fuse and key switch. It looks to be plugged into a dark wire, blue? that runs inside the rubber on the cable from the battery. You will need this wire hooked up. For testing I would just wrap the end of that heavy cable with black tape, from the rubber out over the end of the cable. Don't want it touching anything.
The other heavy cable, just leave it hanging as is, it has to power on it.
The small red white wire I would unplug the short bit of wire and wrap that up with tape.
The small b/w wire is ground, no problem there.
Now with the key on, engine stop switch in run, check voltage at the red/white wire at the coil and TCI box. If they both have power and it's at battery voltage then it should get fire by kicking.
Leo