Fertilising a veg plot

I haven't been able to grow anything in the former hen run, I don't know why. I thought it would be brilliant for veg but nothing thrived at all not even weeds, so there was def something wrong. Have left it for 2 seasons now and want to put veg in this year. Would be tatties turnips & leeks mainly. What kind of fertiliser should I get? My soil is all quite poor ad I live on a slope beside open moorland, and my neighbour told me all the goodness in the soil drains off downhill in the wet.
EDITED- Have had quite a lot of advice from this forum in the past and you helped me get some really nice flowers going ty!

 

I think you will find that the soil may have be high in Nitrogen, chicken poo is strong and can burn seeding etc

I use mainly 20:10:10 in Spring and 5:10;10 in Autum as i can get it cheap, but if my soil is lacking anything i get it tested (which is free for me) and then buy some fert to suit

 

Get one of these wee soil testing kits. will that do?