This sounds like BLOD (blue light of death) it can be hard to pin point what is going on but i suggest that if the PS4 is within its warranty i would get it looked at. however if no there are some reasons this may be occurring.
first lets address the symptoms: Power indicator light pulsing blue, No video/ Audio output and finally the ps4 turning off after the power indication light pulses blue.
some of the reasons BLOD may occur is because of the following:
a power supply issue
a hard drive issue
a general hardware issue
if the PS4 is not within warranty period, look at repairing it yourself via iFixit guides or YouTube