</font><font color="blue" class="small">( What are the little rubber lines that go between the injectors? )</font>
Bill, the little rubber hose going between injectors is called a fuel "leak off" line. Injectors are made so that they leak a little fuel from the nozzle back into the injector for lubrication. After lubing and cooling the injector, this fuel is returned to the fuel tank. Normally, the leak off lines are only a problem if they leak fuel onto the engine. The amount of fuel in those lines is always small and I doubt that has anything to do with your engine's running problem.
I think your idea of draining all the fuel and starting with fresh fuel is a good idea if you have any reason to believe the fuel is bad. Was there a lot of trash when you changed the filter? Your symptoms really do sound like a classic case of fuel starvation. If you can let the tractor sit for awhile and it starts a runs normal for a few seconds, I'd think the problem might be fuel supply. If it starts and immediately runs rough, I'd guess the problem may be in the injector pump. The injector pump probably has a bleed screw for proper bleeding. On my TC45, it's on the side of the injector pump, perpendicular to the outlets going to the injectors. Just opening the input plumbing line may not be enough to bleed the pump properly.
Is it possible you have a loose fuel line and the injector pump is sucking air? In my repair manual, sucking air is mentioned as another reason for an engine to not have power.