Hello MG mate a lot of the LEDs used for the charge light actually change colour so say for charging they will glow yellow for example and then green for fully charged.
Now depending on what sort of LED/s it is either means you have to replace the charging one or the whole thing as some LEDs work on circuitry that will change the colour depending on the stored charge ie volts and theoretical available current.
this may give you an idea on what I am saying https://www.sparkfun.com/products/105
? & Light-emitting diode - Wikipedia, the free encyclopedia
Having said all that to replace is no mean feat you need to be able to disassemble the machine and from experience those LEDs are very small. For what it is worth my friend I would just accept that the fully charged comes on if it doesn't well something is wrong either with the battery or adaptor
Oh by the way I meant to mention my Toshiba's show me when power is hooked up too so in effect I have three LED indicators on the machine