Monitor blank with blinking power light

I have a Gateway GT 5458E running Vista Home premium with Service Pack 2. AMD Athlon 64 x 2 Dual Core 4600" 2.4 GHz, 1.0 GB RAM, 32-bit system with a Gateway Model 900W flat screen monitor.

Recently the monitor quit working. When plugged into a power outlet, the on/off light blinks slowly. Usually, is is a steady blue with powered on, and a steady yellow when in sleep mode. I can't get it to power down, and it stays blank and blinking no matter whether the computer is on or off when you hook the video cable up to is

I have tried the monitor on a different computer (running XP), and it works fine, and have tried another flatscreen monitor on the Gateway computer, and that works fine also. I have also switched the video cables.

Why won't the monitor work with the computer that it has been connected to for three years, but works with another computer, and other monitors work with this computer?

Any suggestions would be appreciated.