Okay, it was a lithium battery, and I took it with me.
I got a Duracell replacement, same number, although it says "Duracell Medical" in it; 3V, just as the old one, DL2032, CR2032, just as the old battery.
I installed it, and after cleaning the interior of the machine, turned it on.
It seems to work fine, but Microsoft did a whole lot of funny things with the screen, such as now only my recycle and firefox shortcut icons show. Also, the clock is off.
What'll I do now?