I just bought a replacement Toshiba Satellite M55- S1001 battery, 6 cell (48 Wh) and have been attempting to charge it for the past 3 hours but the battery charge light/ battery icon on the desktop are not on indicating no activity.
I am wondering if it is a fautly battery, or if something more serious is wrong with the computer which works fine when just plugged in.
He mentions that it works fine with the power cable plugged in, so the power cable is fine. Maybe there is a problem between the battery itself and the charger. I'd try a new battery anyway and see if it works.
If you are having problems with the power connector, it probably needs resoldering to the motherboard - quite expensive unfortunately, but plenty of repair shops can do this for you. Expect to pay £60-£100.
Afterwards, or with your next laptop (!), consider fitting one of our LapTugs http://laptug.co.uk/. These protect the power socket jack connector by giving the lead another anchor point so that any jolts or snags don't transmit to the socket and damage it. V small investment which can save a lot of aggravation!