DIAGNOSIS: The machine is in a safety lock-out, usually because it thinks there's no water. The pump won't engage if the water level sensor isn't triggered or if the thermoblock hasn't reached a basic temperature.
FIX: First, check the obvious: is the water tank full and pushed all the way in until it clicks? Take it out and re-seat it firmly. Then, turn the machine off at the power switch, wait 10 seconds, and turn it back on. Wait for the power light to stop blinking and stay solid (takes about 30 seconds). Then try the brew button.
IF THAT DIDN'T WORK: The micro-switch behind the brew/steam knob might be faulty or have debris. You'd hear a faint click when you turn the knob if it's engaging. This requires disassembly to check, which is a more involved fix.
HEADS UP: If the machine was just used for steam, it needs time to cool down and re-pressurize before the brew function will work again. Wait a minute or two after steaming.