According to Chabad custom, one recites all of the morning blessings even if he did not sleep, with the exception of Asher Yatzar, which can be recited only if one (1) performed his bodily functions and/or (2) slept for half an hour, in which case he is like a new creation. Otherwise [if one did not sleep and is unable to relieve himself], Asher Yatzar is to recited without uttering the name of G-d or mentioning His Kingship.
Nevertheless, the non-Chabad custom is to skip al netilas yadayim, unless one relieves himself, in which case he can say it. Or he can hear it from someone else.
Elokai Neshama – one can hear from someone else.
The blessings on the Torah – one can be yotzi by saying Ahava Rabba and learning after the morning prayers. If one slept 30 min. the day before his sleepless night, he can say it. If he had in mind the day before that the blessings on Torah study should cease to be effective the following dawn, that is also good.
“WHO REMOVES SLEEP, etc.” – one hears from someone else.
Personally, I follow the Chabad custom in this matter.