Yeah, this one's usually simple. First, check the obvious: is it plugged in? The power cord should be firmly seated in the printer and the wall outlet.
If it's plugged in, check the outlet itself with another device. The printer uses a universal voltage (AC 100-240V), so that shouldn't be the issue. Try a different power cable if you have one.
If that didn't work: There's a small chance the internal power supply is faulty. Before assuming the worst, check the rear of the printer or where the cord connects for any physical damage. The power consumption in 'Power Off Mode' is very low (approx. 0.2W), so you wouldn't see or hear anything.
Heads up: This model has a worry-free 2-year limited warranty with registration, including full unit replacement for the second year if you use genuine Epson ink. If it's truly unresponsive and new, that's a warranty claim.