My lenovo T61 can't power on when un plugged from wall socket?

Do you have the Lenovo power management software installed? (Easiest from Lenovo "System Update".) It will give you an assessment of the battery health. Without a spare battery, you can't really tell if the battery has failed - which they all eventually do - or the MB's charging circuitry has issues. The latter will generally be bad news.

Dude its a main thing that your battery is either dead or damaged