Need help determining the problem of of random shutdown?

I have an old MBP which I thought wasnt working so I removed the battery(it was already bulging) and disconnected the LCD screen(it was flickering with purple lines).

I connected it to an external monitor thru HDMI and to my surprise it’s working fine!

I reconnected the LCD screen to try to isolate the problem, and it seemed to work for awhile, there was no more flickering but it shut down just a few seconds after logging in. I was pressing the brightness button when it happened so I thought it might be a power supply problem.

During the restart it kept shutting down before getting to the login screen. the flickering was back.

I disconnected it again and connected the external monitor and it’s back to normal.

I shut it down and reconnected the screen again with the external monitor, surprisingly both screen and the external monitor seems to have NO problem at all! this time I just didnt press anything after logging in, waited for awhile and played with the brightness and played with changing the resolution for both screens. Everything looks to be fixed now????

BUT when I restarted it, while it was loading, the LCD screen started flickering again (the external monitor was not flickering). and then it shut down by itself. :(

So Im not sure whats not working:

1. is it the LCD panel? (but it seemed to work sometimes!)
2. Maybe the display cable that connects the screen to the logic board is defective?
3. Power supply problem? I removed the battery and its connected to the adapter all the time.
4. Graphics card problem? seems to be working fine with the external monitor

Any ideas?