The use of "about" on "discuss" and "think"

There's nothing conceptually "special" about discuss, consider, investigate; that's just how the words are used.

Discuss is always transitive: it requires a direct object. (However, if you hold a discussion it may be about some topic.)

Consider and investigate are usually transitive and take a direct object: you consider or investigate a topic. They may be used intransitively: "John paused to consider", or "John is going to investigate", but a direct object is always implied. (If he conducts an investigation it will ordinarily be of or into a topic. One does not however hold or conduct or anything-else a consideration— that has quite a different meaning.

Think may be either transitive ("Think deep thoughts") or intransitive ("John thought deeply"). If intransitive, it usually employs about with its topic.

There's neither a mystery nor a general principle here, just a bunch of atomic facts you have to memorize.

The grammatical explanation is that verbs like think and look are intransitive. That means they cannot normally be followed by a direct object, but can only be complemented by a prepositional phrase which in the case of think usually begins with about (or of) and in the case of look usually begins with at. (An alternative interpretation sees think about and look at as prepositional verbs which are transitive and which can be followed by a direct object.)

Discuss, by contrast, is a transitive verb which must normally be followed by a direct object. This is supported by the figures quoted by RegDwight in his comment on GuiccoPiano's answer, and the Oxford English Dictionary has no citations at all for discuss about.

This, I’m afraid, doesn’t answer the question of why this should be so. That would require an investigation into the history of each word, which is not possible here.