If the apps that u need data are on sdcard(their datas)then u just do adb pull /sdcard c:\sdbackup with phone on.
if not then:
1ST: IM NOT RESPONSABLE FOR ANY DAMAGE / FAIL WHILE DOING THIS METHOD, I TESTED ON MY FRIENDīS N4 BUT I CANT GUARANTEE THAT WILL WORK ON EVERY NEXUS (INCLUDING YOURS), USE AT YOUR OWN RISK.
2ND: DO NOT CRY IF U CANT GET BACK THE FILES IF SOMETHING FAIL. YOU COULD JUST BUY SCREEN REPLACEMENT OR GET A JTAG DUMP
3RD: do carefuly. if you are nervous calm down b4 doing this. one single command and u can format the nand so be careful.
4TH: I hope it Works for u
5TH: u need to have adb seted up and also drivers. if you dont know how, search google(for drivers).
for adb just install minimal adb and fastboot
6TH: its recomended to test to see if cygwin(u will know what it is in a moment) is working (do some commands on it, like cd .. (to go back)or ls (list files) )
7TH: if u have any errors contact me asap and i will try to help you
unlock the bootloader: (type in cmd prompt, fastboot oem unlock, and follow instructions on phone)(DO THE MANUAL WAY, DO NOT USE TOOLKITS, KEEP READING TO KNOW WHY)(it will say that u will loose files, but it actualy dosent format, it just change the 1stīs block of userdata partition to make it unmountable normally,thats why toolkits do fastboot format userdata after unlock.and tutorials say to format data in STOCk recovery, since custom ones dosent format, just delete everything except sdcard)
(do not format anything, even on stock recovery)
flash multirom recovery:http://d-h.st/pzv
for his great work)(the only that i use, so i cant tell others)
then do this
(instead of doing it with phone on, just do on recovery,adb is enabled on it)
email - email@example.com
skype - abui.ss
Nexus 4 / 16gb - Stock 4.3, soon to be Rmaīd again
New Nexus 7 wifi / 32gb - AOSPA + franco.kernel
Galaxy S3 Intl(I9300) - cm 10.2