Question
Am I able to daven Shacharis if i have not slept the night before?
Answer
You may daven Shacharit even if you haven't slept the night before.
There is a problem though in regard to saying some of the brachot. Therefore, you should hear the brachot for learning torah , "elokay Neshama" and "Hama'avir Shena ..." from somebody else and answer "amen." In regard to the bracha of "Netilat Yadayim", you may say it yourself after you have gone to use the bathroom and wahed your hands.
(see Mishna B'rura 4:30, 46:24, 47:28)
Shana Tova and Gemar Chatima Tova