I'm sorry, but it really doesn't matter who you think should pay. It's the law. It's a federal law, and the school is not in compliance. OP, if it's written in his IEP that he's supposed to have assistive technology available, then they are REQUIRED BY LAW to provide it. FYI, dysgraphia is much more serious than having poor penmanship. It is a very challenging learning disability, a processing disorder, whereby thoughts/ideas in the brain never make it to the page, because writing is a very complicated process. If you don't have this disability, then it just happens automatically. But think of it....you have an idea, what words verbalize that idea, what sounds make that word, what letters make that sound, how the heck do I make that letter, etc. THe process of writing is less difficult when typing.
At this point, I would seriously consider hiring an advocate and request a meeting with his team. Saying that all the alphasmarts are broken is lame. He should have a computer available to him whenever he is required to write, and that computer is to be provided by the school if it is an accomodation in his IEP.