Why does my laptop often have a blue screen?

If it works with the adapter plugged in, then it sounds like a battery issue. If it does work with adapter, I would first run CHKDSK and SFC /SCANNOW to eliminate and drive and file corruption issues.

Then you can persue trying to see if you can get a better definition. But in the end, it is probably the battery.

Try starting it in safe mode and reducing screen brightness to a minimum. All this to reduce power draw to see if he battery can support less drain. It may, or may not. If it does, I think that would eliminate a problem with the laptop. If it does or does not, start with a new battery.