Diagnosis
This is almost always a power supply problem. The internal power board in the soundbar isn't getting the juice it needs, or a component on it has failed.
How to Fix It
First, unplug the soundbar from the wall and from the subwoofer. Check the power cable where it plugs into the back of the soundbar—make sure it's fully seated and not loose. Now, take that same power cable and plug it directly into a wall outlet you know works (like one your lamp works in), bypassing any power strips or surge protectors. If there's still no sign of life, the issue is likely inside the soundbar itself.
If That Didn't Work
If the soundbar itself is dead, the subwoofer might still have power. Check for a light on the subwoofer. If the subwoofer has power but the soundbar doesn't, the problem is isolated to the soundbar's internal power board. At this point, the repair is a component-level fix you'd need a technician for, or it's a warranty/replacement situation.
Heads Up
These units don't have a user-replaceable fuse. Don't try to open it unless you're very experienced with live electronics—the power supply can hold a charge even when unplugged.