Using skill checks can feel very gamey. I'd recommend just letting players talk things out. This should help them get into character, too.
Try rolling most of the non-combat skill checks yourself in secret.
Then let me dissent from the consensus.
Agreed; not a plot hook. I don't want to get distracted critiquing styles of DMs that are happy with their campaign, so I'm going to try to avoid responding to your examples in detail. Instead, I'll just talk about why you'd use the technique of writing plot hooks in the first place.
The purpose of plot hooks is to avoid the problem of the PC's being lost in the sandbox and unable to figure out what will be interesting an engaging.
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Detailing out a setting and brain storming ahead of time and crafting plot hooks to offer to the players will avoid this problem.
I hate skill challenges like 4e. Do your players a favor and ditch them. Rolling dice to see if you succeed "in entirety" at something is just gambling on your stats. Roll means either of two things: success or failure. It just isn't engaging. Combat is technically gambling but players influence the situation without knowing the outcome. This makes it more exciting.
Example:
Lets assume your party has a Lawful Good person with the Background of Folk Hero. They ignore an old man's cabbage problem. You put effort into describing this. Make it matter! Bring it up later during a combat situation:
You're running from the angry mob and spy a nearby cart full of cabbages that would make an ideal spot to hide and catch your breath! An old man who looks vaguely familiar sits atop the cart. As you draw near he looks over and squints. He stands up and shakes his fist at you. This gives you pause and he snarls "You good for nothing whelps! Kids these days! I tell you they got no respect!". As the mob rounds the corner and spots you comprehension dawns and he cackles gleefully. The old fart jumps up and down while waving his arms to draw their attention. As you speed past the cart the old man's voice trails in the distance, "You're bad seeds! I knew it! You deserve whatever that mob is about to dish! Karma's a bitch!"
Now, you tell them that since they didn't get to take a breather they have to make a Con roll to see if anyone has exhaustion for this fight!
Or
Maybe failing to help a wagon fix its wheel delayed supplies to a magic shop in Baldur's gate. Word came that it was raided by Orcs that night and the components the wizard/artificer had ordered were destroyed and it would take another 6 weeks to get a new order in...
Try these out and I guarantee your party will be much more engaged in the non-combat situations you pour your time into.
Try rolling most of the non-combat skill checks yourself in secret. It can improve the experience for the players when they don't know how well they did on certain rolls. It also can help keep immersion for them, because they can just describe what they're doing, while at the same time knowing that their skills are coming into play. You might even want to throw in some references to that so they don't have to just take your word for it.
This doesn't sound to me like a skill challenge presentation issue, but rather an issue of the player not buying into the stakes. Perhaps you might try more overtly discussing the stakes of the scene with the players and giving them some say on what success and failure look like. People tend to be more engaged with their own ideas in my experience and a neat side effect of this is that players will often make failure way worse than you might be comfortable unilaterally imposing. An example might be, "Okay, so the thief is running away with the very important missive. If she gets away, this will be a very bad outcome for you. What do you think happens if you fail in this scene?" Once everyone agrees, run the "skill challenge" in whatever way your group likes best.
If you are of the opinion that the amount of dice you roll constitute the amount of "D&D" you're playing and not rolling dice = "freeform RP", then I am afraid the many of the posts in this thread have wasted your time.
Apologies.
Okay, that explanation kind of got away from me. Basically, iserith, do you have some examples of times you let the party determine what failure would look like? If in my example I hadn't thought of a few end results, I'm not sure I could have done as satisfying a job if I'd just winged it. I made sure to have a town square map ready to go, along with the enemy tokens and stat blocks, should combat break out. I also designed the magic silver ring the PC's now have, including a picture and a hand out, which they think is quite cool.