When switched on at the mains the power light is all that works

On the back panel there is a section labelled Patch Bay
There are 2 small switches which assign each Power Amp to either Monitor or Main Output.
It would seem you have them both set the same at present. Set one to Monitor and one to Main, and use the corresponding Power Amp outputs direct to speakers.

Note you can send signal to external amps or powered speakers from the preamp outputs. This is really handy.
Download and print the manual from https://www.manualslib.com/manual/90516/Kustom-Kpm-8420t.html
and keep it with the mixer.

( Of course don't send speaker outputs to other amps or powered speakers )

Is your graphic eq assigned to main and is kit set correctly?

If you have an equaliser, check that you havent accidentally pressed the button which switches between the main input and aux or bluetooth. Right, if you have aftermarket sound system, check that your RCA's/(look like av cables) arent unplugged broken off or damaged. Another thing is to see if the amps come on (usually shown on amp by a green light) red if not on. Check the power wire from the battery to amp, check if fuse is not blown. Ground the amps properly for the amps to come on and check that the power cable is connected properly as well. Another fault could be blown speakers.

Troubleshooting depends on what skills and tools you have. Since the fuses are located inside the amp, then I take it you're comfortable with removing the lid and poking around inside.

So, taking the usual mains power safety precautions....

Check that power from the wall socket is getting through to the amp. Use a multimeter to check the mains voltage as it comes in from the power cord. Also check the power is getting through the mains switch and on to the power supply board.

Disconnect the speakers and then power up the amp. If it comes on, then you've probably got either a cabling or speaker issue. Double check by trying the amp volume (no source, no speakers) and ramp it up slowly to 100%. If the amp still stays on then look at your speakers.

Connect one speaker, add a source of music. Power up and check the volume again but to about 1/3rd volume. If the amp cuts out then you found the bad speaker/wiring. If it ran okay then try with the second speaker attached. Repeat as before.

If the amp won't fore up with no speakers attached then something is either worn out or blown inside. Disconnect the live mains feed. Be careful of any capacitors. They will probably be holding charge.

Do a visual inspection. You're looking for capacitor bulge (Google it) or obvious signs of a diode, resistor or transistor having either blown or overheated.

Hi, I think in most amps switching to bridge mode simply means the amp supplies its total power through the left channel only. It's the best way to use all of your amp's power but nothing comes out of the right channel. Having speakers connected to both channels would simply mean that only the Left channel works, it would not blow it. Some amps have the speakers wired to binding posts and this varies according to whether you want mono, stereo or bridged. I can't help with the power board sorry

Sounds like a Electrolytic capacitor has failed. Search backwards from the speaker connections inside the unit to the main PC board. Replace the first ones that you come accross that are linked with the speakers.

Check the headphone socket if it cuts out the speakers (normal use) when you plug the headphones in. If it doesn't and you have a switch to switch off the speakers when listening to headphones, check the switch. It may be physical damage or dirt causing the problem, or even loose soldering on the headphone socket. But the fact that headphones work shows the main amp is working. Also make certain the speakers are connected properly.

on ur subwoofer u will see HPF output, connect this output to MAIN IN of ur power amp (first remove jumper between pre-out and main in from ur power amp) connect pre-out of ur power amp to input 2 L&R (Left is also for mono input). the HFP selector switch will cut off 80Hz or 100Hz to the main input depending on the position enabling u to have high frequency sound on your main speakers. connect the speakers to the main output terminal of ur power amp. do not connect speakers on the woofer ouput.
make sure u are using the right impedance speakers. do not switch speaker impedance selector while the unit is on. 

The bypass switch in the headphone jack is likely broken. NEVER unplug the headphones while the amp is on.

There are certain small amps that have a possibilty of popping the power amp due to a feedback arrangement. Likewise, never use the headphone jack for ANYTHING other than headphones.

I would Initialize Unit back to factory settings by turning off main power switch then hold both 6.1/7.1 surround and direct buttons ( they are next to each other near main power switch) in while turning un main power switch. Hold both buttons until you see all lights light up. Then check functions and setup like you bought it new.
Owners manual also explains how to initialize receiver