have you tried pressing on the back of the tama? It could be a problem with the insides not connecting properly and causing no picture at all.
I had this problem with my first Tama and when I kept pressing the back casing it re-appeared! If it's faulty, take it back to where it was bought if possible.
In fact, today mum is taking my tamagotchi back to Toys R Us (I'm poorly and have to stay at home) to see if we can have a refund or a replacement Tama. I bought another Tama anyway (this time lemon-coloured with pink, blue and purple flowers!) and the new one is working perfectly.
I grew really attached to my first one, I had cool characters, I got the little starfish shaped guy, then the little apple guy. I also earnt quite alot of points pretty quickly! Poor Nanou.. *cries*