I've had this frustrating problem with my SONY VAIO VGN-FW590FWB for a very long time now.
I received this laptop as a gift. I was happy with it and for awhile and used it with no problems, until suddenly my battery began to have issues. It would not hold charge for long at first, and then eventually not at all. I tried swapping out the battery with a battery from the same model that a friend had with no success, it wouldn't charge. After awhile of using it using adaptor power, the laptop shut off and wouldn't turn back on. I more or less got discouraged and left it in a corner and forgot about it for a few years and relied on my desktop until I recently decided to come back to it to see if I could use it, as aside from the battery problem it was still in very good condition. I tried on a whim, connecting the adaptor from my SONY Vaio all in one desktop (also purchased around the same time) to the laptop. What do you know, it booted up, so I realized that not only the battery had failed within a year of purchase but so had the adaptor. But I figured, at least I knew the solution and so I went and purchased a replacement sony adaptor and battery. I plugged the adaptor in and installed windows 10 and then when the battery arrived in the mail I plugged it in to charge and everything seemed fine. I let it charge to 100% then shut it off for the night. Today I turn it on again to use it and I notice that the battery is not charging and although it says it is 94% charged, when I unplug the adaptor it immedietly shuts down. I don't know what to do at this point. There seems to be nothing physically wrong with the laptop, and my attempts to install the updates from the sony vaio website have been unsuccessful. It's an older model, but it has barely seen any usage since the day I got it because of this problem and has similar specs to my desktop, which works great. Customer support at sony has been extremely unhelpful in even figuring out what the problem might be and just told me to go spend money at best buy to "see what the problem is". This is ridiculous, to say the least.
Also to note, the light next to the battery symbol on the front of the laptop is blinking orange when the a/c adaptor is plugged in.