If the non-custodial parent continuously doesn't pay child support, collects unemployment now and then for the past 2 years (only support that has come in) but then decides to move out of state and go to college. Is he still responsible for support during this time? Would the courts go after him for not paying support?
If he goes 90 days without a payment, the child support office can go after him, but he times it so there is at least 1 payment every 90 days. Is there something that can be done about that?

They should have attatched his unemployment. Also how is he attending school with no money?

As long as there is a child support order in place, the father is responsible for paying support. Enforcement is a different issue.