viability of parsnip seed is very short. year at most. so you have to use the freshest seeds. All seeds have germination temperature, temperature range for the seed to sprout.
Parsnips are one of the harder ones to sprout. If you do a search, most will tell you to plant three seeds per "hole" and that's about right. Needs rich soil. Need to keep the soil moist. Need to keep temperature warm 24/7. may take a month or so to germinate so be patient.
I start harvesting my parsnip in Nov, Dec. Makes them sweeter. Same goes with spinach. Great winter veggies. If you want to try now start in a germination tray with electric heat pad underneath. prep and get a cold frame or greenhouse/hoop house ready. lots of compost loose fryable soil to depth of 12" or more. When the seedlings are 2 inches high or so, harden off slowly in the cold frame/greenhouse then after about a week or two, transplant.
Parsnip takes about 120 days to maturity. so slow growing.Have to be patient with them.