I haven't played Dawn of the New World, but based on my experiences with the first one and an understanding that it's acknowledged as being intrinsically inferior to its predecessor...
Pick up Rune Factory Frontier. I'd probably recommend Harvest Moon: Magical Melody before that, but of those three listed I'm gonna recommend Rune Factory.
I actually did try Harvest Moon: magical melody and I quite liked it. I just wanna see some opinions on whats good and why, as maybe ill like ToS or Rune Factory a little more than Harvest.
On a side note I played harvest magical melody for like 8 hours straight on the Wii but for some reason it didnt save. Left a sour taste in my mouth! This was proably a month into owning my wii, which would have been a few years ago.
This may be a stupid question, but did you have a Gamecube memory card? You need one to save Gamecube game files! Also it has to be in Slot A, rather than Slot B.
Honestly, if we were talking about the original ToS, Rune Factory Frontier, and Magical Melody? I'd probably recommend Frontier, still, but only because of the combat. I would recommend it above the others without hesitation if it weren't for the Runey system. If you can get Runeys to work for you, then Rune Factory is wonderful. Otherwise, you might like Harvest Moon more, but I hear Tree of Tranquility is pretty bad as far as Harvest Moon games go.
Tales of Symphonia gets a lot of love on this site, but I don't think it's up to par with the other two games mentioned - and it doesn't have any farming, so that's another problem.