Then it's likely either a bad power supply or motherboard.
Power supplies put out different voltages on the different connectors, so you can get fans, lights or both running, but there isn't any or enough power getting to either the motherboard or the CPU.
I would start by replacing the power supply, it's fairly simple and there are many youtube videos. If that doesn't work you can typically return the power supply without any fuss and then you may be looking at replacing the motherboard.