Minitor/Computer cannot be powered on if DisplayPort cable is connected

Hello

I’m using my Studio XPS 13 connected to an HP LA2205wg monitor via DisplayPort (DP).
However I cannot turn the computer nor the monitor on if the DP cable is connected. Both power button do not work.
If I disconnect the cable I can turn the monitor on as well as the computer. Connecting the DP cable after does not bring any problem - actually it is the unique way to turn on the computer/monitor.

What is strange is even if the laptop is not powered (power supply is not connect) I still cannot turn the monitor on. Only if the laptop has no energy source (ex. without battery) I can turn on the monitor with the DP cable connected on the XPS.

I tested it using VGA and everything goes fine. I assume that this is a DP problem only and it seems to be a hardware issue. Nevertheless may also be a configuration issue but I already went to the monitor options and no success. Since the problem happens before the computer is powered it cannot be a software issue. I cannot say if it DELL or an HP problem without at least testing the XPS on another monitor with DP. 

Had someone any similar problem with DP or even something similar with HDMI?

Thank you in advance