Most batteries for Lenovo have a membrane test button on the bottom of the battery which lights up to five blue LEDs to show the battery state. That will indicate whether the battery is duff or there is an issue within the machine if the battery is not charging.
Also look carefully - Thinkpads were notorious for the yellow power inlet socket coming loose or falling off its bracket completely. Inserting the power plug in such circumstances might result in a poor or no connection. Reattaching the connector is quite easy once the case bottom is removed.
The alternative is to find the specific desktop docking station for your machine on which the laptop stands and makes connection through the long connector in the middle of the base. The attachment then gives you extra USB sockets, things such as VGA/DVI/HDMI and sometimes parallel connectors, P/S2 mouse and keyboard connections, ethernet, and - above all - another power inlet.