Teardowns I've Worked On
Answer to: Replace digitizer or lcd or bothChange the whole LCD with digitizer assembly is more easier. Here is a blog showing how to replace Z2 LCD, hope it does help. http://www.witrigs.com/blog/how-to-change-sony-xperia-z2-lcd-screen/
Answer to: mobile is not rebootingTry to charge the device for a while, then see whether it works.