It's not the monitor, it's the video card or video drivers. The video card is sending garbage signals to the monitor, so it goes into sleep mode as it doen't "know" what else to do. The reason the older monitor worked is that it doen't pay any attention to those signals. Silly question, I know, but did you read the instructions that came with the monitor? Some have a trouble-shootiing guide, not restricted to things like "check all the leads are connected...".
First thing to do is to reboot in safe mode, and check settings. too fast a refresh rate is a common cause. Other possible reasons are an IRQ conflict between the video card and another bit of hardware, NIC or TV card maybe.
Many people aren't aware that installing an updated driver for the MONITOR can often cure such problems, but concentrate on the video/graphics card. Go to the manuf. site, if possible, to see if they have any available.