Which phone? And which "button" do you mean? The home button to wake up the screen? Or the power off/on button to turn the device on or off?
Most phones that I have used require you to press and hold the power button for a few seconds(3-5 seconds) to get the device to turn on or off. A quick press usually has no effect, but pressing and holding for a few seconds, then releasing allows the phone to power on or off.
If you mean the Home button to turn your screen, that just takes a light tap ... if that's not working it may be a defect in your phone. How old is the phone?
The other possibility is the Accessibility settings were turned on requiring at least two taps to select and to open the apps or widgets.
I'm most definitely NOT a VZW employee. If a post answered your question, please mark it as the answer.