LQM® 10.8V 7800mAh New 40Y6797 Laptop Battery for Lenovo IBM ThinkPad T60 R60 R500 W500 T500 SL300 SL400 SL500 40Y6795 42T4619 42T4620 92P1133

I recently got a replacement battery from Amazon for my T500 and it seems to work well enough. Cost about $26 USD from a seller named LQM which you can check out here: https://www.amazon.com/dp/B0FBRCG1P1 "Should i give to a third party technician and chnage the cells or buy a new one?" I forget which batteries have the bullshit mechanism that Lenovo put in place but iirc a part of the battery needs to stay powered or it'll brick itself when you replace the cells. Something to research and keep in mind if you go down the route of re-celling the battery you have.