Here's a situation that's come up twice for me now. The obstacle card Power Failure reads:

"The lights in this room refuse to turn on. Place a darkness marker in your room. Solve Wiring Puzzle #1A to discard this card and the darkness marker to continue exploring this room."

So what happens if the investigator has a Torch or Lantern on them? Those cards read: "Investigators may ignore darkness in your room." So the question is, Can someone use a lantern to just bypass the puzzle and find what the darkness was hiding? (a skinless man, for example) We ruled that with the lantern/torch, You COULD skip the puzzle to get the items/clues beneath it, but the room remains officially in darkness unless someone goes ahead and solves the puzzle anyway. I'd love to hear what everyone else's take is, though.

Bonus Queston: if you have an Axe & find a Lock puzzle, can you roll to break the puzzle as soon as you locate it, or do you have to at least TRY the puzzle first then smash it next turn?

If the players were behind the clock or there were only 2 of them or something I could see giving this to them, but I don't think it is wrong to require them to solve it either. The lantern would still let them 'Explore' as an action and not an action + move.

Realistically... not sure who all has been in caves and experienced total darkness... but a torch in complete darkness is not worth that much. Its a million times better than no light, but you aren't finding hidden objects, small objects, or anything like it. The best you are likely to do is see something that looks like it is worth investigation... looking at it in better light. Restoring some light to the room and then being able to take MORE light (torch or lantern) into the dimly lit corners to search is pretty darn realistic IMO.

I don't think any of these places are ever really bright to begin with... and total darkness is... total!

If you want a decent reason for someone with a lantern to still have to fix the wiring problem, you could just explain that whatever else is in the room is in a safe with an electric lock, or something to that effect. The darkness could be ignored, but they still can't get to anything worthwhile until they're able to bypass the lock by fixing the electrical problem.

In the proposed case above, the Lantern would negate the penalties for the Darkness token, but the investigators are (due to the card) prohibited from continuing to Explore while that Darkness token is in the room.

Yep, as they say above... the card specifically states that you can not continue to explore the room until the darkness counter has been removed... not negated.

Also... you have to spend an action to use the axe against the lock, so as you have to explore to reveal the obstacle, you can't do it right away. You might as well try the puzzle to see if it's an easy solve (we had one where half of a combo-lock was solved just by flipping the tiles), and if not then you can use your action to cut the lock off.