Laptop batteries and cordless tool batteries are the prime sources. Usually, only one cell fails prematurely and the others are salvageable.
I have been doing this for years; one cell powers a
LED lamp perfectly, and direct charges from a 15W
solar panel, if you monitor the voltage and disconnect at 4.2VDC (it's been a while) or pop! and your cell is dead.
There are always ads on Kijiji looking for these as freebies, so you have competition. But the source is massive; it's just a matter of tapping into a network.
Also, hook up with Freecycle sites.
Volunteer at your
local thrift shop.
The third -- and trickest -- source is municipal recycling depots. They have become very strict when it comes to scavenging electronics -- both for liability and privacy purposes. So, you're going to have to go James Bond/Mission Impossible on this (let the theme song run through your head; it helps).
Fourth, hook up with a not-for-profit that takes discarded corporate laptops and repurposes them for low income folks. The batts are usually toast; if you can build trust, there's and endless supply chain, and you do something good in the process.
Matching up cells to prevent overheating when charging is a very delicate business. I assume you are well aware that you are constructing one of the most effective firestarters on Earth, if anything goes wrong? Respect it like a big container of
gasoline with a built-in ignition system and you will be fine.