When clicking on the 529 Plan contribution under New York, the system bugs out and logs off. What's going on?

[Critter-3]

That is a known issue ... Much of the NY program will not be operational until 1/13 or later so come back then. 

https://care-cdn.prodsupportsite.a.intuit.com/forms-availability/turbotax_ny_windows_individual.html

The feds will not start accepting returns this year until 1/24 so you have time to wait ... don't be in a rush and file an incorrect return.