Pressing the display's power button does not turn off the display nor put my Mac to sleep. Instead, holding the button just makes the power LED brighter than usual.
That's normal with the DVI to ADC adapter. ADC (Apple Display Connector) has pins for power control but there are no such pins in DVI so the display's power button has no way to control the computer. I don't know why the power light brightens when pushed, but mine does it too.
Two USB ports on the back of the display doesn't seem to work. It does charge my iPod, but any device connected to those ports (including iPod) won't be recognized on my Mac.
Is the adapter's USB cable plugged into the computer? The displays ports are USB 1.1. Some devices, such as iPhones, require USB 2.0.
Failure of the USB circuitry is common with those displays. My 22" ADC display started having USB problems years ago. It started with intermittent USB port problems, then it started interfering with computer sleep. Since I now use the display with a DVI to ADC adapter I don't connect the adapter's USB cable (and don't use the display's USB ports), so don't have any computer sleep problems.