Hello,
I've watched a lot of period dramas but I think they were all about relatively recent periods. What I'm looking for is something set like at least 3000 or 4000 years ago. The older, the better. I do not mind from which country it is.
Hm...I don't know about 4000 years ago...but this is the oldest kdrama you can find probably as it's set in around 60-50BC and follows the Life of the founder of the first real "country"/dynasty/everything we know as Korea today. He is considered the grandson of a water god, so that just goes to show how old this legend/real life story is xD
 http://mydramalist.com/661-jumong
Jumong does sound like what you might be looking for - it's a marvelous blend of adventure, romance, politics and a hint of fantasy, with fast plotting, great characters, gorgeous cinematography and expensive production values.
I agree with Jumong. I am also trying to watch and finish Emperor Wang Gun, 200 episodes. It's the start of Goryeo Dynasty. 
http://mydramalist.com/1123-emperor-wang-gun
Thank you everyone but I've already watched Jumong. (Apart from the last episode. I couldn't bear to see it end ^^) I'm looking for something older than that, not necessarily a korean drama. Chinese maybe? They have quite a long history.
I am afraid either Korean nor Chinese dramas do not touch so "ancient" times like 3-4k ago (tho it would be interesting).

Probably it's because, there is not many written evidences from that time and it would be hard to came up with the story if you don't even know who lived there ;)

Nevertheless, there are some topics, which put dramas on historical time table so maybe it would be helpful to you to find out which one is set the most "far away" time :)

Chinese: http://mydramalist.com/discussions/chinese-drama-m...
Korean: http://mydramalist.com/discussions/korean-dramas-m...
Japanese: http://mydramalist.com/discussions/japanese-drama-...

It seems the earliest Japanese drama is from Yayoi Period (300 BC - 250 or 300 AD), Chinese one from Spring and Autumn Period (71-476 BC) and Korean from Goguryeo (37 BC ? – 668 AD)