Based on the image, I would start with an inventory.
- Hands, fingernails.
- Shirt, Belt, Pants
- Torch (Split into Club, Metal Bits(shielding), Flame, Fuel Source)
- Potentially any loose material (Mud, potential Rock, rock bits)
- Hair.
To be honest, the torch inside the room seems out of place. Based on the logic you spoke about, who would put an ad-hoc version of a flaming mace in a prisoners cell?
Not that you'll take that suggestion, but I'll present some ideas that presume the torch is not in the room, however there still is one across the hall, well out of reach.
1, Gain rope.
- - Use Belt
- - Turn Pants into shorts, by tearing strips off and tying them together.
2, Gain Torch
- - Tie Lasso with rope. hook it on the torch across the hall. pull it back.
3, Gain Rock
- - feel the wall around the room, bumping pieces of it, until you find a lose piece. work with it to remove it.
4, Gain Tools.
- - Hit the metal of the torch with the rock until it breaks off. Makes a lot of noise, brings guards, losses fire/light.
5, Gain Tools with less noise.
- - Blow out the torch and wrap your shirt in it. Loses light. Now hit with the rock, quieter, but not quiet enough. Guards still come, though you get a moment more.
6, Gain dirt.
- - Scrape dirt off the ground, corners, walls, etc... Collect a small handful of it, presuming damp/mud like.
7, Gain tools with near silence
- - Repeat step 5, but this time place the dirt under it, to make less noise from the ground impacts.
(Given the nature of the game, you might want a worry bar, essentially a bar that rises as you worry about guards, traps, etc... I.e. too much noise, coming up to a corner, etc... Even though it won't do much for the game, players will quickly learn that it helps measure their actions, and they can choose lighter actions when replaying the same area. (presuming numerous devastating fails.)
8, Gain Tools and Fire with near silence.
- - repeat step 7, but carefully remove the fire/fuel source first. - presume a split of a Wooden club, a metal bowl for holding the fuel, and the metal wrapping that also helps hold the fuel/fire, but now you can see light earlier.
9, open the cell.
- - use the metal bits (tools) to open work with the door. - doesn't work, guard comes by notices torch, you die.
10, Open the cell better.
- - Put the fuel/fire back into the metal bowl and carry that to hold the light. pick the lock, Before completing the lock pick, the bowl gets too hot, AOOHH! your drop it clank, guard comes, you die. (essentially all my plans leave you defenseless, even with the club, until you can get out of the cell instead of being a fish in a barrel.)
11, Open the cell, succeed.
- - Repeat step 10, but this time carry the bowl in the fabric from your shirt. it lights the way and doesn't get too hot. This time, you pick the lock before a guard shows up.
12, Open the cell door
- - CREEEEEEEAKKKKKK! loud creaking noise brings guards. But you don't have a club in hand
13, Open the door quieter
- - Squeeze the dirt clump to get a finer mud liquid out, directly over the hinges, and work it into them. When opening, there is still a noise, but not as loud.
You should leave the room with a club, a metal bowl of fire, a rope looped through your belt (from your pants shreddings), metal bits, and a bit of mud (where to put it though)
- - Bit of dirt is in hand under bowl of fire?
- - Bit of dirt is smeared all over you as a bit of camouflage?
If you have the dirt clump it can be thrown in eyes/face of a guard to distract them.
Some additional possibilities.
1) Sleeping guard just down the hall, keys or weapon in ropes reach?
2) using belt or shredded pants rope, produce noose, be ready for guard as they pass. (this would be for more of a brawl type game)
3) Use the metal bits to remove the pins from the door hinges.
4) Complete the first part, attempt to reassemble the torch, put it back on the wall, use dirt to stuff up the key hole, so it doesn't latch again and shut the door. Wait for the guard to pass and then follow them quietly.
- - This helps with the idea that if you get out, and go the direction that the patrolling guard is not, you will find it takes you almost immediately to a guard room, with others, armed. then the patrolling guard calls out about the empty cell, and you are trapped in the path of both sets of guards, with nothing but a small wooden club for a weapon.
- - If you follow the guard, you come up to the same spot, but now, they thing that way is cleared. To make their rounds, they will leave out another entrance. While they are distracted, you can take things from the edge of the room. like a weapon, shield, change of clothes.
- - With a changes of clothes and some batting material (could be other clothes or bags) you can sneak back to your cell again, setup a dummy in your old clothes, that looks like you sleeping in the corner. Wait just out of site. until the guard passes again. Now, you can escape without sounding an alarm. Or at least you can progress farther before that point.