This highlights the need for one of the most simple troubleshooting tools of all time, pictured below:
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This type of tool is available on eBay, Amazon, and at your local auto supply or hardware store. With it, you could check your fuse in just seconds, by attaching the clip to ground, and touching the probe to either side of the fuse. If the light lights on only one side, you have power to the fuse, and a blown fuse. If it doesn't light on either side, your problem lies closer to the battery. Often times if the load (In this case the inverter) is switched on, placing the clip on one side of the fuse and the probe on the other will tell you if the fuse is blown. If it lights, the fuse is blown. This is not a sure fire method, but it's quick and easy, and then you can move on to the next step. Obviously, you can also check the power right at the inverter with the same tool.
Everyone should have this basic tool, at the very least. If you do, there will always someone willing to step you through the troubleshooting process. It's much simpler to use than a meter of any kind, but it's only good for simple troubleshooting.
By the way, my inverter has 10 fuses inside all connected together for a total of 200 amps. So if you're having any good luck, the device may still be ok, but the internal fuses are blown.
Be extremely careful about opening up this type of electronic device. They have large capacitors which can retain a charge fore a long time, and accidental contact can result in a shock, or serious equipment damage.