Try soft reseting your phone. If that doesnt work then try hard reseting. To soft reset take the stylus pen and push in the little hole on the bottom of the phone. You should feel a little click and then your phone will restart. Wait until your phone starts up again and if it still isnt working then do a hard reset.
To hard reset, hold down the green send button and the red end call button at the same time and continue to hold them down as you then push your stylus pen into the hole on the bottom of the phone untill you feel the little click. Your phone should start to reset. Be warned you will loose any information saved to the phones memory ie: phone numbers, pictures, personal settings. Anything saved to your memory card should be ok.
If your screen remains blank after trying both resets I would suggest taking it back to where you got it and and have them fix it or replace it.
Hope this is helpful.