I'm still having this issue too even after switching to the new ZTE Valet replacement phone I was sent. I have tried everything mentioned here and it still will not power on at times until I take the battery out, then put it back in. It doesn't happen as often with this new phone but, it should not be happening at all!
I am seriously looking for another smartphone that doesn't have this problem. I know I'll have to pay more than the $50 I paid for this one. It will be worth it to not have to worry about it powering on. I have seen some good deals on other phones with more options and larger screens. I always read the customer reviews and more than 90% of them are positive.