Well the not turning on without being plugged in is likely a battery issue. However the other sounds more like there is a problem with the laptop. First I would try starting it up in "Safe Mode" and see if it loads fine then. While you will have restricted access in that mode, if it loads better, then there is something on the device that is the problem. Bad program, malware, virus, etc., which would have to be removed to resolve the issue.
If, however, it still gives you problems loading in "Safe Mode" as well, then I would be looking at it being a hardware issue.
How to enter "Safe Mode" when booting the computer.
In Windows 8 and 10...
As your computer restarts, press F8 (possibly a few times) to enter "Safe Mode"
a. Press the...