I don't imagine you have an oscilloscope to look at the 24V DMX data signal...
If you have a multimeter, you can write a little test program to slowly
toggle the data line and check if it's going between (approx) +24V and zero.
I'm not really familiar with the DMX specs/requirements, so I'm not sure about any of this... But, it looks like you are supposed to have a balanced ("push pull') connection. Is that right? And, I think
you are not getting enough current through the 10k resistor. Do you have any idea about the current requirements or the input impedance of your DMX devices? (RS-485?) The more devices you hook-up, the more of a problem that 10K resistor becomes.
A lower-value resistor might "work", but you probably need a better driver circuit to drive
the signal high, rather than relying on a pull-up resistor. Unbalanced drive might "work" too, but I don't think
it's compliant to the spec. You should be able to get an RS-485 driver chip.