Those reasons are good.
Besides giving them reasons, here are some things you can do to help convince them:
1) Demonstration. Since you are not a salesman (or saleswoman), your parents are unlikely to be persuaded by clever rhetoric about why your piano sucks and why you need a new one. Instead, demonstrate to them its shortcomings.
2) Be specific with your request. Rather than saying "I need a new piano!!", say something like (just an example), "I got to look at one of the new Kawai uprights and they seem really good, and our piano is getting rather old... those Kawai pianos are also very affordable and durable, and retain a lot of their original value in case we need to sell it later." This is much more convincing. It also shows that you did your own research, which saves them time (and money). Parents like that.
3) Show them (in some clever way) that you've earned it. Prove that you deserve a new one, and that it will be put to good use. Make sure you don't go overboard on this one.
And most importantly, 4) Make it very obvious that until you get a new piano, you're going to bug them constantly for one. Sooner or later they'll have to give in!
- Saturn