Why might the dash and tail lights not work on a 1989 Buick Century?

Answer 1

Answer
it could be because one of your tail lights, brake lights, reverse lights, etc. the dash light goes off to let you know this. there is nothing wrong with the dash, probably. then again i have also seen minor electrical parts fried that cost an immense amount of mula. try the lights new answer
i hit a deer once and that same thing happenned to my '88 century. I ended up replacing a fuse in the dashboard fusebox that, in the manual that came with the car (if i remember correctly) did not directly correspond to either the dash lights or rear lights. only after checking ALL the fuses and after the replacement of this supposedly unrelated, yet obviously blown fuse, they worked.
My wife decided to jump start another vehicle during our ice storm and burned the contacts in the light switch.. which was the contact to bridge the dash/taillamps

New answer:
I had this same problem with my 1990 Century. All my lights worked (except dash/tail) and my fuses were good. Replacing the head light switch took care of the problem. I hope that helps