The battery in my laptop starts charging normally. Then after a few seconds the LED turns off and the battery stops charging.

I have a problem with a Toshiba laptop model M55-S325. When I plug the power cord while the laptop is turned on it starts to charge and the AC power LED turns on as well as the charging LED. Then after a few seconds the charging LED turns off and the battery stops charging but the AC power LED stills on. If I unplug the power cord and plug it again it happens again.
I also noticed that this happens only while I’m in Windows. If I charge my laptop turned off it charges normal. Also during the boot and loading of Windows the charging is normal. I checked the power jack and I don’t thing the problem is there. I move the power cord while connected to check for failures in both the jack and the cable and in both cases the laptop turn off and on but nothing happened, everything is the same. What do you think the problem might be? Please help.

Can the laptop run just on the battery power, when the AC adapter is unplugged?
The problem with your laptops is very similar to a battery charging problem with some Toshiba Satellite A105 laptops. Almost the same symptoms. In case of Satellite A105 the problem could be resolved by upgrading the BIOS version. I think it might work for your laptop too. Go to Toshiba tech support website and download the latest BIOS for your model. It looks like at this moment the latest version is v2.10
You mentioned that the charging problem occurs only in Windows. I think it might be somehow related to Toshiba Power Saver software. Try to reinstall the power saver.
If upgrading the BIOS version and reinstalling the power saver software will not help, you might have a hardware problem. In Satellite M55 the battery connects directly to the system board. So, it might be either the battery failure or the system board failure. The best way to test it is finding a spare battery and test the laptop with the new battery installed.