Laptop Won't Turn ON after shutdown

My laptop does not turn ON after I shutdown my laptop. The only option working for me is to remove the battery and insert again. After the shutdown, If I don’t unplug the power cable, then I am able to turn it ON. Please Advise.

Will it run without the battery ?

Yes.

Does it run normally ? Just run it without the battery or buy another battery..

It runs normally without battery. I am also able to run with battery alone, if I reinsert the battery. So if there is problem with battery it should not run. The battery is the new one I purchased two weeks back. Last week it worked fine. What do you think?

Is the battery charging ? Now days you really don’t need a battery since you have to plug it into the wall most of the time anyway. If it works fine with the battery out and in, then there must be a problem somewhere is the power switching… Do you have your power switch to laptop ?

The battery is charging fine. So I have to run my laptop without the battery inserted and put in battery whenever needed.