Since inverters work by massaging a ~12V DC input voltage into 120V AC, it stands to reason that your inverter won’t work if it doesn’t have a good connection to your vehicle’s electrical system. So the very first things you’ll want to do, if you haven’t done so already, is to verify that the connection between the inverter and the electrical system, or auxiliary battery, is solid and that the electrical system is in good working order.
For cigarette lighter inverters:
Check the socket for obstructions.
Check the socket for potential shorts like paper clips or small coins.
If the socket is clear, plug another device into test it.
If the socket doesn’t have power, see: Why Doesn’t My 12V Socket Work?
For battery-wired inverters:
Check for power and ground at the inverter.
If the inverter doesn’t have power or ground:
Check the power and ground wires for corrosion and shorts.
Check any in-line fuses or fuse box fuses if present.
Even if the inverter has power and ground, it may fail to work if the battery and electrical system aren’t in good working order. Some inverters will give a warning, either via an indicator light or warning tone, if the input voltage is too low, but that may not be the case with your particular unit. Of course, if your battery is on the way out, or your alternator isn’t charging properly, those are definitely things you’ll want to get taken care of before you head off on a road trip anyway.