My father passed away in 2002. I have begun this year receiving notices from PA about state taxes due but not paid in 1986. He had no assets at all upon death (not even a house) and was in a nursing home on Social Security. What do I do? Do I have to pay these or does my mom have to pay? Will they be forgiven?

Your mom would have to pay them not you but then it may depend on if her name is attached to it in any way.
If her name is not attached let them know he has died and see if they say your mom is then responsible.

Take a look at the tax notice.

If it has ONLY your father's name on it, then ONLY your father (or, in this case, his estate) is liable for the taxes.

Since his estate has no money, you should contact the Pennsylvania Department of Taxation and inform them that your father is deceased and that his estate has no assets. They may ask for a copy of the death certificate. Once you provide the death certificate, that should settle this issue.

YOU will have to pay NOTHING.