Diagnosis
This is almost always a power supply issue. The internal power adapter or the connection to it has failed.
How to Fix It
First, check the basics. 1) Make sure the wall outlet works by plugging in something else. 2) Trace the power cable from the soundbar to the small black power adapter brick. 3) Check that the cable is fully plugged into both the brick and the soundbar. If it all looks connected, the adapter itself is likely dead and needs to be replaced. Polk doesn't sell it separately, but you can find a universal 12V DC adapter that matches the specs (center-positive polarity, 12V, at least 3A).
If That Didn't Work
If a new adapter doesn't fix it, the problem is inside the soundbar, likely on the main board where the power connects. At that point, repair isn't really practical for most folks.
Heads Up
Never force the DC plug into the soundbar's port. It only fits one way, and forcing it can damage the internal power jack, which is a much harder fix than swapping an external adapter.