Diagnosis
This is almost always a tripped internal thermal safety cutoff. These heaters have a backup thermal fuse that can blow if the unit overheats, sometimes from a clogged filter or being placed too close to a wall.
How to Fix It
First, unplug it and let it cool completely for an hour. Then, check the air intake on the back. If it's dusty, vacuum it out thoroughly. Plug it into a different, known-good wall outlet (not a power strip) and try turning it on. If it's still dead, the internal thermal fuse likely needs replacement, which requires opening the case.
If That Didn't Work
The issue might be the power cord or internal wiring. Check the cord for any kinks, cuts, or damage near the plug or where it enters the heater. A break in the cord can cause a complete failure.
Heads Up
Opening the heater case to replace the thermal fuse voids the warranty and involves working with mains voltage. If you're not comfortable with that, Vornado's customer service is reportedly good for troubleshooting and repair options.