these are the exact symptoms of a corrupt EFS, and because you don't have a backup your phone is screwed and you will need a new motherboard. always backup EFS the moment you get your phone... That's what everybody says.
If I were you in this situation I'd salvage as many sellable parts of the phone (screen, battery etc), and use the money to buy a completely new phone. Otherwise I will just send it in for replacement
Sent from my Nexus 5 using Tapatalk
Current - LG Nexus 5
, franco.Kernel r11, Cataclysm ROM
Current Tablet - Ainol Novo 7 Aurora II
, CyanogenMod 10.1 Unofficial
Sony Ericsson Xperia X10, CyanogenMod 7.2 Unofficial, spoilt battery
Sony Ericsson Xperia arc S, Stock 4.1.B.0.587, lost back cover, spoilt microUSB port
HTC HD2, NexusHD CM10.2
Apple iPad 3 - iOS 6.0 Jailbroken
Minimalistic Holo Blue Whatsapp+ Theme
Nexus One boot animation for Nexus 5
How to Change DPI?