I am encountering the same issue with my Hanns-G HG281D and a GTS250 XFX card.
I just upgraded from a 8800GTX that worked fine, but now the monitor remains on "check video input" when the PC goes into standby or when its shutdown.
asus crosshair mobo (latest bios with S1&S3 acpi enabled)
Hanns-G HG281D Monitor - connected using DVI out to HDMI in, on the monitor
XFX GTS250 GFX with clean install of latest nVidia drivers installed.
Win7 Ultimate
The standby feature on the monitor worked fine on the eVGA 8800GTX card I replaced. Connection DVI>>HDMI was the same as well. I have not bothered with DVI>>VGA because the last time I used it, it looked horrible, so if that is what it takes I won't use the card. ha ha
Extremely frustrating, I already forgot to turn off my monitor once, an had 5 1/2 hours of "Check input" square sitting in the middle of my screen.
EDIT: I tested a DVI>>VGA cable I had laying around, an that of course works fine. Not a surprise really. But I can notice a text quality and color vibrance hit easily just looking at my desktop. Either my cable is of poor quality, or my screen is just big enough to tell the difference. The monitor will standby in win7 and when the PC is shutoff when using that cable. So it is for sure linked to the HDMI input factor. At least in this case. It just baffles me that it worked fine on the older card, but the newer one is giving me issues.