My advice even though you bought a new power supply of 600w of power output.
Is to stay away from power supply units that are not recommended as main stream good PSU.
Ones of little known brand names, I have never heard of a Ewent EW3905 power supply unit.
The general rule of thumb here is if the power supply unit was very cheap to buy for a claimed 600 watts of power output.
Is that it should be treated with suspect that it cannot output no where near the actual 600 watts it quotes.
The exact test to this, and guess what. is to put the system under a heavy gaming load.
There is the Irony believe it or not, if the system becomes unstable, powers off completely all of a sudden, or resets it`s self while performing a load test it speaks for it`s self on the possible problem.
Given you also have a problem with the system also failing to power up properly I would say it was the case of a weak and miss quoted cheap PSU posing as a high quality one.
For alot of people when it comes to a power supply it is the most common thing they tend to skip on to do with the pricing.
But it if anything the most critical component of a PC before anything else.
Paying up to $100 or pounds for a well known and branded power supply in the long run is about the best thing you can ever do or buy when building your own system, I cannot stress how important it really is though you may begrudge the cost of buying one priced so high.
Most people end up doing the worst option to try to save a bit of money considering a PSU not to be one of the critical components of a system build. But there wrong.
And it`s where you learn the hard way on how important it is to pay the extra or high price of a well branded Psu with the specifications quoted on it to be the truth.