How to fix sony xperia z: Won't turn on but led light glows blue when plugged to pc

[Finnick]

Also, when I plug it to the charger, the screen repeatedly vibrates then starts to turn on but shuts down again (with red led light). How do I fix this?

[Uliwooly]

That seems more if a hardware issue, but try this

Connect your phone to a wall charger, press and hold power and volume up for 10 seconds, let it charge for 2-3 hours

[John-BR]

Hi @Finnick

Welcome to the community.

Have you tried the options on this page? 

http://support.sonymobile.com/global-en/xperiaz/faq/I-cannot-power-on-my-device/

[AmirSherlock]

dude thanks it happened to me just now and it worked! thanks!!!

[Izzy64]

I kept doing the press volume up and power on , it took about 5 mins but it went back on