I had a similar problem. There are loads of how-to vids on YouTube, but while you can apparently solder (thick-ish) leads between each cell, the ideal solution is, apparently, to spot weld metal straps between each cell. As I don't have the gear for spot welding, and the soldering idea CAN be a bit dodgy (according to some of the vids anyway) I gave up with that idea and have finally done nothing. Though apparently, soldering NiCads is less dodgy than soldering NiMh and LiPo cells.
There are companies who will do that job for you (with spot welds) but the postage is v costly - more than the cost of a new drill in my case.
And there are also vids on YouTube on how to make your own spot welder, plus spot welders to buy on the bay.
To me anyway, the whole idea became very unattractive, so despite hating to chuck "good" stuff away, I gave up on the whole idea.
P.S. I had similar "sessions" re the dead rechargeable cells on a domestic vacuum cleaner and eventually came to the same conclusion.
But that's just my personal decision. I still have the subject drill and one day MAYBE I'll convert it to run off a mains-fed 12 V transformer - one of these fine wet days!