...And I thought I was the only one this happened to. I experienced this at least several times, but I had contributed it to accidentally getting it wet the following day that I got it. But from your testimony, it appears that mine wasn't an isolated incident. And like yourself, I would repeatedly press the button a number of times until I got power.
Fortunately, that, along with a non-working camera button, I was able to return it to the Sprint store I bought it from and got a brand new replacement free of charge that very same day. Although with your situation, I'm not sure why your Sprint dealer would have you wait so he can order it. If they're selling them to other customers, then that means they have an extra one to swap out for you. Maybe they're just being cheap about it. If I were you, I'd raise a stink about it and demand they give you a new phone on the spot. After all, Sprint is still making money off of you while you hang on to that inoperable phone during that waiting period.