Hi!!
So the blue light turns on and then the PS4 turns off?
This could mean 2 things..
1: faulty power supply! You can replace this one and see if it works, if not, return it and get yourself a refund.
2: APU issues! This one isn’t fun. There are multiple solutions to solve it, but they are not easy.
A: reflow! You can reflow the APU and see if that worked! This is most of the time a temporary fix, but cheap.
B: reballing! Replacing the solder under the APU! This one does fix it most of the time. But it’s the most difficult fix and it requires special tools.
C: replacing the motherboard! This should fix it for good. It’s very easy to replace it, but , is the most expensive one as well!
If you need any guide, please let me know!