According to the archival glossary:
Dexterity 0 means that the character cannot move at all. He stands motionless, rigid, and helpless.
He does not gain paralyzed condition and thus no specific game rule limits him to purely mental actions or prevents him from talking. Thus, we must fall back to natural English meanings of the words.
My interpretation would be that he can cast spells that are purely mental, or ones that require focus / material components he is already holding. Given that section on verbal components state:
A silence spell or a gag spoils the incantation (and thus the spell).
I would interpret that being forced to be motionless spoils such components just as well. On the other hand, as a player I would accept ruling either way on that point.