Hello, I've been having trouble connecting my Xbox 360 to a DVI monitor (Acer x223w). I'm running an HDMI cord from my Xbox to a female HDMI to male DVI connector straight into my monitor. The monitor says "no signal" before going to sleep, and it won't bring up the menu unless it's receiving a signal. If I unplug the HDMI and plug it back into the Xbox, it will come up with "No Signal" again on the monitor.
The issue could be with the display setting of your xbox. If you have it too high, then it will not register a picture. Youtube how to reset your xbox display settings, i think its hold right trigger and Y, but not 100% sure. This should fix it.