How can I solve the problem?

Hi!

First things first! Did you already tried the basic things (just to be sure)?

1: Tried to get in the Recovery menu? Are you able to get in there? If yes, please try to restore the system from there.

2: Tried to use a other hard drive? Does it stay on with a other hard drive? If yes, then replace the drive and install the PS4 software on there.

3: Tried a different power outlet and power cable? Did this solved it?

If all mentioned above didn't work then read further!

If none of the above worked, then most likely it's deeper, the most common issues regarding what you described:

1: Power Supply issue

2: APU issue

First I would buy a new PSU and replace it and test it. If this didn't fixed it, then I would return the PSU and ask for a refund.

If the APU failed, then please reflow the APU and test it afterward. In my experience a reflow is a temporary fix (it still can works for years, but will fail eventually) and thus reballing is needed (or replacing the APU). Not sure if you are familiar with soldering? Otherwise you could bring it in to a local repair shop to ask them to do it. It's difficult, but it's doable.

Guide for replacing the PSU: PlayStation 4 Slim 電源ユニットの交換

Good luck and let us know how it goes!