I am trying to reproduce your issue in our lab but I am not able to. I was wondering if you could send me the BIOS version information for your Lenovo X201 system.
My configuration is as follow:
System - Lenovo x201
BIOS - 1.31 (6QET61WW) I also tried v1.36 (6QET66WW) and v 1.37
Intel AMT Version - 188.8.131.522 and v184.108.40.2067
DTK version - 7.0.11161.2
So far I have tested 3 KVM solution (ouside of the DTK) and they work as well. I think we just need to figure out what is different between my system and yours. Once we can figure that out, we can start working getting your system up and running.
Lets try booting the system into Safe mode and see if the mouse and keyboard work with your KVM solution. Since we know now it is not a DTK, RealVNC, UltraVNC or TightVNC issue we can start focusing on the client you are working on. I am suspecting that the issue is going to end up being a driver issue.
Also verify that all firewall settings are turned off.