Thanks. :p
In the past I have taken these batteries apart and frankly do not want to deal with anymore lithium fires.
Which flashlight is it? Being AAA I’m assuming a twisty?
Yeah it's a twisty.
Which particular flashlight…brand make model
As last resort, A tiny hole in base could free it up.
Brand new cell, I don't have any way to hook it up to a circuit as one end is stuck inside the flashlight.
It is a modded maglite solitaire.
As long as the water doesnt short it, I dont really see a problem.
Try the wooden dowel with a different adhesive like hot glue or gorilla glue. Super glue doesn’t work well with wood…
maybe roughen up the surface of the negative side then solder a thick copper wire and pull it out.
Or just send it to energizer to get it fixed or replaced,
Heck, use magnet & wires to complete the circuit to an incan bulb. LOL, more work so far than the base is worth?
Maybe buy another Solitaire and put the incan head on the L91 to run it down. Put the base on the mod light for good, or till you run it down and drill it out of there.
PS - Kreisler, you are too funny with those posts and deletes. The shame of it. 
What about a firm tap on a piece of tubing (same dimension as the light) attached to the end of the light with a piece of tape. Don’t fix the light but prepare a pillow for it…
Scaru,
Remove the head and tailcap. Remove the bulb so the switch assembly is exposed (part #8 in diagram below). Using a needle, get under the flat lip you can see on the switch assembly and pry up at several places. The switch assembly is in two halves, the larger part inside and the outer part (flat disk the bulb prongs push into) and are held together just like in the minimags. Anyway, pry off the outer top part then you can use a metal rod or something that fits into the hole and knock the battery and inner switch out the back from the front. It WILL work. Make sure you don't lose either of the small metal contacts. Once you get the battery out you can put the inner switch back in, and connect the outer part to it like it was. Reassemble the rest of the light and try with a different battery.
You don’t need access to both sides for it to work.
combination of wd40 + tide rope twirling and banging it on wood!! just might get lucky, i dont think heating or freezing will do anything to be honest lol. but seriously law of physics what goes in must come out!! unless u smashed it in snuggly!!
Scaru
How did it turn out ?
There are very few problems that the suitable application of high explosives can’t solve… 
It's on the way back to energizer. :)
JohnnyMac method worked for me. The problem was not corrosion but that AAA batteries vary slightly in width. My Duracell battery was too tight so I smoothed out the inside of the Maglite battery compartment with a cylindrical file until a replacement battery would slide in and out easily.
Cheers
Jeff
Though it won’t work on lights the principle still applies. Look into “bullet pullers”, the inertia or hammer kind. Devise something similar and it would work I think. And no chance of damage to the open end of the light! Just don’t ask me why there’s now a long brass rod and a small hammer in my shooting kit, OK?
Phil