If a clockwork construct has both intelligence and its own key, can it wind itself?
Like the damascene drow... It has 13 intelligence.
Clockwork keys are not fixed on the creature, they are just like door keys (see some examples) and each will fit into a different creature. As such, they may be taken away, usually by their creator. Though a single key may work on several clockworks.
This is explained on the general bestiary entry for Clockwork creatures:
Clockwork creations, as their names suggests, must be wound up before they animate. The creator of a clockwork crafts a unique key for each creation. This key is typically inserted into the clockwork’s back and turned clockwise to wind it. Turning the key counterclockwise has the effect of winding the machine down, though only a willing (or completely helpless) machine will allow itself to be unwound in this way, meaning either its creator or someone its creator has specifically designated can normally do so. Since each key is totally unique, construction of a new key (or bypassing a key entirely) requires a successful Disable Device check (DC = 20 + the clockwork’s CR). Larger clockworks tend to have larger keys, and particularly huge keys require more than one set of hands to turn. Rather than seek assistance from other engineers, eccentric or hermetic inventors often rely upon other clockwork creations to help them turn keys or aid in the creation of more monumental constructs. Other times, engineers give copies of keys to their most trusted clockworks, which can be programmed to wind allies and even themselves as the situation requires.
This explains how it works in general. Most clockworks, if given their own key, can wind up themselves or even allies. But without a key, they can't do anything. There may be exceptions to this, like clockworks that do not require a key, or even those who cannot wind themselves.
I know of one example on a published adventure path (Mummy Mask #3) where the clockworks may wind each other, but not themselves. They were given their own keys and are the standard clockwork servants (which have no mention of this), but they were built in a way that it's impossible for them to wind up themselves, so they were given orders to wind up each other and guard a certain place.
Considering Damascene Drow has the ability to apply maintenance on itself
While not requiring food, drink, or sleep, the automaton requires periodic maintenance to their body. This process takes one hour of time and involves cleaning components, adjusting fit of gears and repairing any damaged parts, and reapplying lubricants. This requires an hour of time and a Disable Device (DC15). Failure results in needing to repeat the task. The automaton may do this procedure to itself, but the difficulty of the Disable Device (DC25) rises and an additional Sleight of Hand (DC25) check is required due to the difficulty of reaching parts.
I would say you can do it with a succesful DC 25 Sleight of Hand check made to be able to reach your winding part. In this check you can take 20 as there is no penalty for failing to do it.
The general rule for Clockwork Construct is:
Winding: The construct must be wound with a special key in order to function. As a general rule, a fully wound clockwork can remain active for 1 day per HD, but shorter or longer durations are possible.
Nothing about the clockwork being unable to do that itself, so it would be able to, under the conditions you stated.
About the damascene drow... actually it is not a Clockwork Construct but a Clockwork Automaton. However it works quite the same:
Anyone may wind an automaton, provided they have a key, or the necessary skills to complete the task.
Anyone, so it includes the automaton itself, if it has the disable device skill (the damascene drow gets racial bonus in it, going easily to +14 by putting 6 ranks, more than it needs to succeed at the DC20 check by taking 10).
Clockwork automatons also need maintenance but this part is explicitly possible to perform by the automaton itself (but with increased DCs for the skill ckecks).