toshiba satellite 1620CDS acting weird with battery

Hi. I found this laptop from the "mountain" of discarded laptops which was basically only for untested and wrecked laptops for 15 euros each... Very nice surprise because this was working and the condition was even great.

Anyway, it's still acting weird with the battery. Basically, when battery is inserted, it always tries to start computer using only battery, whether the power source is connected or not and obviously can't start with empty battery. Only when I disconnect it, and plug powers source after that, it uses power source to power up. after booting with power source, I can insert the battery and only then it starts to charge it! But as soon as I unplug power source, it starts to use battery... but even after I plug power source again, it won't even notice power source and still continues using battery only!

So when I have full charged battery (amazingly keeps power just fine for a long time!) and disconnected power source, to be able to use power source again there is no other way than just shutdown the computer, disconnect the battery and boot with with power source and only after it power up, I can insert the battery and it starts again to charge it again.

And weird enough, when I use my universal laptop adapter set with proper connection and power of 19 Volts, it won't even start at all. But if I use another IBM power source with only 16 volts, 4.5A (toshiba uses 19 volts!), it starts with it just fine! I doubt it is because of the ampere because the multiadapter set says 19V uses 4.7 Amps.

So I am now wondering, where the problem lies... battery or the computer itself???




EDIT: NOW I CAN'T EVEN CHARGE THE BATTERY. EVERY TIME WHEN I INSERT THE BATTERY, IT USES IT IMMEDIATELY AND "DISCARD" POWER SOURCE AND SHUTS DOWN BECAUSE OF LOW CHARGED BATTERY!