This answer is just a complement to Dhammadhatu's wonderful answer, and it's a response to your new question added after editing the OP.
You ask about how, for instance, liking a car can lead to dukkha. Well, first we have to figure out what does "liking" mean.
To like something is to find that something likable; to find something likeble is to perceive some sense stimuli as pleasant. To perceive some stimuli as pleasant is to get in contact with a stimuli coming from and object, in this case, a car.
When you like something, two things are happening:
1) You create a concept which represents certain phenomenon (in this case, "car" is the word used to describe the sum of the parts of the car) and endow it with fixed features and qualities. And if the mind is fettered by ignorance, then your perception of such concepts also will include subjective adjective of value, i.e. you will see that concept (a car) as something nice, likable, good, desirable, etc. And if you are get more demanding, you will get obssessed only with certain kinds of such concept (certain kinds of car, with specific shapes, colors, features, etc.). In all these scenarios, you are getting attached to points of view about what is nice and what is not.
2) You can get obssessed with the sensorial features of the concept (the colors, the shape, the smell, the sound, and everything else about the car), because they gave rise to pleasant feelings in the past. In this scenario, you get attached to sense stimuli.
So, in the example given, when you like a car, you're getting attached to feeling (sensations) and points of view (about which things are good and which bad).
Attachment and clinging of any kind lead to suffering and dissatisfaction. When attached, you find something desirable and you don't want to let it go; you want to keep it for yourself, permanently. But the thing is, conditioned phenomena are in constant change, and those things will not stay the same or with you forever. This is why is so important to pay attention when craving arises, because if you let it keep its course, you will probably get attached to the object of desire.
EDIT: In my opinion, this is an excellent question, but I'm not sure if gos against the site's rules to keep expanding the question. Regardless, here are my two cents.
The "funny" thing about dukkha and dissatisfaction is that you will never get to a point where you say: it's over, I don't need anything else. One craves not because the object itself is desirable, but because we keep feeding the tendency and habit of craving.
Maybe the prince will keep its car for a long time, but some things that might affect the car are mostly still out of his control: an earthquake or a fire destroying the car, a thief stealing it, the knowledge of a car which is (according to the point of view he's attached to) "better" and "more desirable", etc. Or maybe nothing of those things will happen. But if the problem is not the car, something else will be, eventually: his health, his youth, his appearence, confrontation against his points of view, the control over his kingdom, and so on.
In sum, craving will never cease with the object of desire themselves. And so, when the object of craving and attachment goes away, dissatisfaction, stress and suffering will arise, in a greater or lesser degree and intensity. Craving only vanishes when the tendency of craving is uprooted and when ignorance in general is extinguished for good. And the training given by the Buddha in the Noble Eightfold Path is the way to achieve that end.
Kind regards, and welcome to the site!