I prefer to think of a script kiddie as...

They just cruise around looking for the latest premade exploits, and collecting them if they happen to work for them. In an earlier stage they go looking for an A-B-C guide to getting into Hotmail or something. In advanced stages they learn to compile things.

But an overriding characteristic is the idea that it must already be out there, and that just knowing it (an exploit someone else made) exists and having it is a way to increase their self-value, and that if it can't be done quickly, it isn't interesting. In other words, a low tolerance for 'hard work'... Although that is not always true, if they have an overriding feeling for vengeance or to right actual or percieved wrongs.