Several times I've brought packets of parsley seeds (both the flat Italian & the curly English parsley) from Australia to Thailand and attempted to grow parsley here, but nothing ever grows. Yet parsley does grow here. The other day I bought 2 big bags of beautiful dark green curly parsley in Big C at Khon Kaen. So what's the secret? What are the parsley growers who supply Big C doing that I'm not?

I have brought celery in Big C, that was imported, I would say so is parsley, I have grown parsley in the UK, like a lot of plants grown in our countries they will not grow over here, just too hot like now, or like our land in the rainy season, just to wet.

I have grown parsley, and other herbs from home, here from time to time. I usually start them in small pots in a protected environment (coolish area/no direct sunlight). Once the plants are hardy enough, I plant them out into a shaded parted of the garden. Too much of this sun and they simply bolt within no time at all. I live in Korat by the way. It is possible, but requires a little more effort (shaded area, shade netting, etc.). Try again and good luck. 

You definitely need to do some research about the correct temperatures for seeding and growing parsley. Also the temp of seed storage could be important. Just a hint for your start