You can only use new seed. The seeds spend so long in the soil that you can grow radishes to maturity between the rows before the parsnip cotyledons are seen. And if it is too wet, or too dry they won't germinate. Too hot - or cold. Then there is the possibility of pest damage.
We now germinate our young parsnips in paper cylinders in the greenhouse. We can control moisture levels, temperature variation, and keep a general eye out for them in the weeks they take to show.
Then, when they have little leaves showing strongly we plant them out in dibber holes in the soil.
The system has proved so reliable that we now have a parsnip glut and we are having to resort to making parsnip wine ! Desperate measures indeed!
I sprinkle three seeds into each tube and then top with peat free potting compost. Watch this space.