I've seen this sort of thing happen when digital signals are allowed to "float" - that is, they're not connected to either a high or a low voltage. What happens is other parts of the circuit leak voltage to where the level is close to the threshold point so any slight variation caused by transistors switching or electromagnetic interference can cause the circuit to think it's been activated on and off.
If indeed it's being caused by an open circuit - which it sounds like it is, since you said it happens even with the digitizer disconnected, that would indicate that the new digitizer is bad; the motherboard is still seeing that signal in an indeterminate state whether it's connected or not. If it stops when you plug in the old digitizer, that would pretty much prove that the new one's no good.
Best of luck with your repair; let us know what you find.