Philogrobolized

Meaning: Cotgrave, definining Philogrobolizé du cerveau, or philogrobolized in the brain:

intoxicated, astonied, bedunced, at his wits end.

Usefulness: 1 (Besides that use, there's also the one suggested in The Horologicon: "It conveys a hangover, without ever having to admit that you've been drinking.")

Logofascination: 1 (Sir Thomas brought it into English, and has the only citation in the OED, but Rabelais might've formed this. It's related to metagrobolize - tomorrow's word - and the OED suggests that the philo- is the traditional compound, meaning love, but I suspect that it is meant to suggest philosophy or philosophising; their brains are overcome by too much thinking. I must admit to also being rather fond of the phrase philogrobolized in their brains.)

In the wild: no; the only other uses I've found are in other translations of Rabelais, or, as mentioned, The Horologicon.

Degrees: 1 (Again with the dilemma! Sir Thomas certainly gets citation rights in the OED, and is possibly responsible for creating the English word, but it already existed in French; this is where the sola tag comes in handy.)

Connections: n/a

Which is used in: G&P, Book the Second, X: How Pantagruel judged so equitably of a controversy, which was wonderfully obscure and difficult, that, by reason of his just decree therein, he was reputed to have a most admirable judgment. The only time Rabelais or Sir Thomas use this word; Pantagruel has bested all the sophisters of Paris, and his reputation has spread. There is a particularly difficult law case which has caused a number of learned judges to be:

at their wits' end, all-to-be-dunced and philogrobolized in their brains,

As per the chapter title, Pantagruel judges it with great wisdom. You might recognise those synonyms from Cotgrave, above; Rabelais was satisfied with philogrobolisez de cerveau.