Superuser does not show prompt
Izzy's comments lead me to correct path, so I have managed to root the device. If somebody else having the same problem (auto-root programs don't work but you can access device using adb root), here is complete how-to to root your phone manually:


Install Superuser from ClockworkMod on Google Play directly to your phone
Prepare adb as root and make /system writeable: adb kill-server, adb root, adb remount (you might need to kill adb.exe in task manager if it hangs)
Pull the just downloaded apk to your computer: adb pull /data/app/com.koushikdutta.superuser-1.apk (note: it may have different name in the future)
On your PC: open the apk using zip (for example rename extension to .zip or use WinRar)
Copy from zip system\bin\su to your working directory
Push it to your phone: adb push su /system/xbin/su
Be sure that owner is root: adb shell chown root:root /system/xbin/su
Set SUID and SGID bits on the binary: adb shell chmod 06755 /system/xbin/su
Reboot phone: adb reboot
Try su from adb: adb shell, su; prompt should change from $ to #
Try su from phone: install terminal and use command su or use Root Checker Basic from the store
If su from adb works but does not work from phone, repeat whole process from 1 but download different Superuser application from market (for example ChainsDD's version didn't work for me)