File and pay NOW. You will be charged interest for any taxes still due (not withheld or otherwise already paid) and a penalty for late filing. If you cannot pay all of what you may owe now, pay as much as you can and see if they'll do an installment agreement for the rest.
How does someone forget to file their state tax return?
It works like this....they do free file for their federal return, and then find some other way to do their state return, discover they owe money, and then decide to wait. Then they forget. They may remember and forget again, and then may bury their head in the sand.
I have actually seen quite a few people do that. They end up coming to me to file their state return and end up paying almost as much as they would have had to pay if I had just done both for them.
Of course that varies from state to state, but in my state I have to do a complete federal return in order to do a state return...the figures intertwine.