Computer will not start first thing in the morning.

You say you turn off the power at the power point.

What is meant by power point?

Flip off your power switch at the end of the night or when your done with the pc, flip the power supply switch on and push the power button on the PC in the morning when you want to use it. See if that works.

You should be using a surge protector to plug your pc into which then goes to the wall socket, when you`re done with the PC, turn off the surge protector, when you flip the surge protector on your pc should start up with no issues.

Never plug a pc directly into the wall socket, if that`s what you are doing.

If you still have issues, then either the power supply is bad or going bad or the motherboard is going bad.

The Zalman should be under warranty, try to get it replaced.

Well then, maybe the computer is tired and like all of us, does not want to go to work in the morning

I'm still not sure what a power point is.

By chance is a power point the wall socket, a extension cord, surge protector or maybe a circuit breaker box??

Yes it helps.
Remove your cord from the wall socket and the power supply.
Inspect both ends and sockets for any signs of damage or burning and aching.