Power button doesn't stay engaged, this is a new problem. I had just don't a load and started the next load and the power button wouldn't stay pushed in and lights go off.

try new switch

It may be a micro switch that is not engaging. Try pushing on the door to see if that solves the problem. If so, put in a spacer to push the switch more.

Either the starter is defective or the ground wire is not on tightly!

It sounds like the switch might be broken. It might need to be replaced.

You don't mention the year, make and model of the vehicle so, my answer will be as vague as your question.
A gasoline engine needs four things to run: fuel, spark,compression and combustion.
When you turn the key does the starter engage? If no, check for power at both sides of the fuse when turning the key.. If there is no power at the fuse when turning the key, go to the ignition switch. You have isolated your problem.
If there is power at fuse then, go to the starter relay. If there is power going into and, going out of the relay then, check the starter. You have isolated your problem.
If yes, check for fuel, spark (plugs and wires), compression(block, pistons, rods, Intake and gaskets) and combustion (small scale explosion from compressed fuel and spark, thus pushing piston).

Your problem may be with a passive anti-theft system installed by the manufacturer. I wouldn't know because you didn't mention the year, make and model of the vehicle.
Your problem could be with a collision based fuel shut down system installed by the manufacturer but, I wouldn't know because you didn't mention the year, make and model of the vehicle.
Your problem could be with any number of common issues related to a specific vehicle; issues that may been discussed at length on this very site but, I wouldn't know because you didn't mention the year,make and model of the vehicle.

the clicking sound is due to the relay is getting turn on but doesn't stay because of bad component in the power supply board or in the main board. you must check first the bridge type diode and FET transistor using an analog or digital tester.

A clutch that's failing doesn't behaves like that - it slowly starts slipping until it fails completely and definitely. If it would break suddenly (like when the pressure plate would snap) the noise and the vibrations it would generate would be unbearable.
No, in your case something is failing inside the transmission/gearbox - most likely in the command forks and their locking pins. The gearbox will have to taken off the car and dismantled to investigate and fix that, and it will be expensive.

check the power supply and rem or proccesor

I think that's Demo mode.
I got stuck there too.

This is what worked for me:

1. Power the radio off (hold the power button in top left corner in for several seconds)
2. Remove face plate
3. Hold in reset 10 seconds
4. Press push-menu dial/button 3 or 4 times
5. Insert cd and hit source to switch to tuner before cd starts

Not all of these steps may be necessary.
I suspect having the power off before the reset button was the important part.

bad start switch on motor, rare. that model # came up as maytag range not a dryer.