I'm in the process of turning my Toshiba Libretto 110CT (a subnotebook from 1998) into a simple remote terminal (over ssh) with custom server software to handle emails, rss feeds, chats and so on. It runs under FreeDOS and connects to WiFi by a combination of PCMCIA ethernet adapter + mobile router with built-in battery. I love the form factor and the "oldschool" keyboard, I have regenerated the battery and it's quit…
Have you any info about how you regenerated the battery?
In a typical "failed battery" there's rarely more than one dead cell in my experience. And I've had packs with as many as 9 cells.
From there, it's a matter of putting it all back together. There's soldering involved, and you have to be extremely careful -- hit the battery with the temp required to melt the solder for too long and you have a seriously dangerous situation on your hands. I use two 3D printed clips and alligator clamps to hold the wire, wand and battery at distance from one another, battery on the bottom, wand on the top, wire in-between, and a 120mm fan, requiring me to only hold the cable to the wand and the length of solder.
Can't caution enough that it's exceedingly dangerous soldering this kind of battery. I originally built the rig because I wanted to improve the quality of my soldering -- I'm pretty terrible with an iron, but I made several changes after I had a small number of batteries start failing after repair and a few searches led me to believe I may have damaged them[1] with my poor soldering skills. My rig involves two 3D printed clips, one to hold the iron exactly where I want it, and one to secure the battery. The cable to the iron has a length of wax lace on it to let me pull it back up/remove the iron from the rig with a yank at a distance.
I use an alligator clip to hold the wiring in place and a long length of solder so that I can stand an arms length away. The iron "drops" in -- it's mounted on top, battery on bottom, wire in-between -- so I can heat it up an inch or so from the battery, I place tip of the length of solder in its spot and "tap" the wire of the iron to drop it into place. When I see it melt the tip of the length of solder and the small amount that's on the wire, I pull up on the string to move the iron away, wait a few seconds so the 120mm fan can cool things a little, and put a new battery in.
Goggles, gloves and a nearby fire extinguisher of the right kind are a really good idea. I also do the work in a large, mostly empty, shed with doors that, when opened, eliminate nearly an entire wall and work directly on the cement floor.
A lot of devices use 18650s and not all 18650s are the same. The one powering your drill might be able to handle higher drain than the one that came out of your laptop; don't mix those up. I was given a cardboard box full of dead laptop battery packs from the same model, so I was taking cells from a similar source each time.
[0] I use an adapter that lets me power a Raspberry Pi via an 18650.
[1] And likely made them into a fire hazard on their own.