A blue colored blank screen appears after login, with working cursor. Nothing else is showing up.

I am using HP 15 ay503tx, with Kali Linux in dual boot mode with Win 10.

Initially the problem was that the GUI was not showing up during login, only text interface was opening asking for login and password. I followed one of the threads on this forum which said:

login to tty1
apt-get update
apt-get upgrade -y
apt-get install -f gdm3

After it, I was able to get the login page properly but after typing username and password, it is showing a blue colored blank screen. I've tried startx and init 5 commands, but nothing is working. I don't want to loose my data. Can someone help me out?

Sounds like a video card/driver issue. Anything helpful in the output of dmesg, /var/log/, or journalctl?