Well, for starters, I'd say don't use D&D. It is a game tailored towards violent conflicts, which is exactly what you're avoiding, it seems. Mind you, I said "violent conflicts". No story, thus no game, can exist without any conflict whatsoever. I'm not also saying it's completely undoable with D&D, just mainly... a waste of its design and practical goals. Another way to put it, to use a metaphor, is: smartphones are great, you can do a lot with them, they're like handheld computers... But they can't really substitute a desktop computer in every way, maybe not even most ways.
Now, if you're willing to work outside of D&D, there are some good systems out there for that "action and adventure doesn't mean swinging swords all the time" vibe you're after, like, for example, Fate (The Dresden Files RPG, Spirit of the Century, Diaspora, etc), in which most of the mechanics about resolving conflicts are the same, regardless if it's a brawl, a wardrobe and style show off or even an economic dispute between Lex Luthor and Bruce Wayne. It's worth a look, really, and there are SRDs available for some of those games (Spirit of the Century and Diaspora, iirc).
If you're sticking to D&D, plotting the campaign isn't the difficult part; the difficult part is to design encounters (which is just a way of saying "conflict scene") that allow your PCs to shine doing their thing when most of their sheets are geared towards combat (yeah, players do that, it being the game it is).
For the wizard (most hocus-pocus folks, really) and rogue, that's easy. Most other types, though, will rely purely on RP, most of the time, which isn't bad per se, just kinda unfair, since some players get to look at their sheets and say "I can do this, this and that", while the fighter's player has to memorize lines from Gladiator and the ranger's player has to become a living Bear Grylls encyclopedia.
If your group can pull it off, that campaign'd be the stuff of legends, but it'll be hard, really.
The Good Approach - Subtle hints were the best way
You mentioned subtle clues, but really that is the best approach. So, they inspected the well and the door, and you already said there is nothing different. Maybe there is something on the wall that hints, perhaps scrawled by previous failed adventurers "Generosity is to be praised." "Each only gets one." Etc.
If they really don't want to bash the door in, maybe they should backtrack get an NPC minion and have the minion make the needed wish.
If you want to be even more subtle, they notice something about the layout of the whole room that reminds the bard/wizard/cleric of some ancient Rune and they should go back to talk to an expert who can then subtly (or not so subtly) hint about it talking about the Rune referring to self sacrafice or something like that.
Speaking of Bards/Clerics even PC Bards and Clerics make a decent way to deliver hints. The Bard remembers some lore suddenly (especially if he hasn't made that check yet), for a Cleric the deity might literally give them a bolt of inspiration. I think this is a distinctly inferior approach, but it may be better than the next options I list.
Slightly Less Good - OOC hints
There is nothing wrong with giving the occassional oblique out of character hint. "Sometimes you just need to take the risk of a trap being there."
Deus Ex Makes it Go Away
This is substantially less good, but you can always make the problem almost literally disappear. A massive earthquake destroys the door, and collapses the well.
Retcon
This is a last resort, but its not necessarily a game breaker to just say openly, "This didn't go the way I had planned, why don't we try this scene again." And if they haven't figured it out, drop some further hints this time around.
Best Answer
There are actually a few solutions, but nearly all of them will touch upon a subject of ownership. I'll try to list a few steps that can help you feel comfortable with their past.
Talk to your players.
Privately or publicly, whichever works, unless they are not sharing they backstories. Probe and ask until you have an idea about how much they care about their backstory, how deeply it affects them as players. You are saying that until now none of them provided you with such. That hints towards your players not caring deeply about this sort of things. Sure, they might now - and that you need to find out.
Establish ownership
Even if just for yourself.
You are the owner of the world. If a backstory of one of the PCs describe a major event that nullifies the whole premise of war, would you go with it? Probably not.
Remember that you can amend backstories. Anything that would spoil your world in that 15 pages of bio? Talk to the player, explain what breaks your setting.
Do you consider backstory characters, like said teachers, families etc. NPCs or PCs henchmen? If latter, then you are effectively equipping them with a herd of supporters that the PC has mind control over. How would you establish a fratricidal feud against one of the PCs if said brother is controlled by your player?
Proceed with common sense and moderation
Your players are consenting adults, no pun intended. They are aware that during the war peaceful villages burn and it's not a GM's sadistic vendetta if it happens to their village.
Try to establish key characters, the ones that "drive" your PCs. They are the ones that you need to treat carefully. Ask your players a few generic questions about "What would your [significant character] do?". When handling those characters adhere to that, with exceptions (see next paragraph). The rest of the characters are going to have an impact on the PCs, but will most likely not break them.
Follow Situation-disturbance-resolution scheme
It's alright to drive PC's brother crazy and make him fratricidal, because he feels that PC abandoned his family (where in fact the PC was just late to the scene). Unless it's completely unreasonable, try to accomodate backstory NPCs into the story as major NPC (that you frequently act out) only if you change them in a way that represents the new status quo. That way you will be safe from acting them out wrong, but still be able to create a interesting situations
Stick and carrot
This gives you a great opportunity, especially if a player is attached to his backstory. My bet is on the PCs trying to "restore order" and "fix" the situation. This disturbance is actually much more compelling for the player that usual carrot. Ever tried to take away your archer's favourite bow? Ever threatened paladin with frown from his deity? Try, but don't go over. The idea is not that they have to lose everything. Threaten, make them uncertain. Make them consider their backstory going away without explicitly making it happen. News are the village has been pillaged. Beloved teacher once again drafted into the army and sent to the front. Brother sends a message that he deserted, now hiding. Make that something present, make the players consider that things at home are not going well, without actually executing their past. They don't care? You can play with those NPCs as much as you want. They do? Even better, take advantage.