Is one to recite Birchas Hatorah if he did not sleep at night?
One is to recite Birchas Hatorah even if he did not sleep at all the previous night. [There is no need to try to hear the blessing from another person.] However the blessing may only be said starting from Alos, just as is the law regarding Birchas Hashachar. [If however one slept at night a standard sleep then the blessing is recited even prior to Alos, if it is past midnight. If however he only slept a temporary sleep it is considered as if he has not slept at all, as explained in the previous Halacha, and thus the blessing may not be recited until Alos.]
Which Alos is one to follow with regards to saying Birchas Hatorah?
One is to be stringent in this regard to follow the opinion which states that Alos begins 72 minutes prior to sunrise. One may learn Torah until this time arrives, even though it is past the Alos of other opinions [90 minutes and 120 minutes].
May one continue learning past Alos, prior to reciting Birchas Hatorah?
One may not continue learning Torah past Alos [of 72 minutes], and thus he is to stop learning and recite Birchas Hatorah. However some Poskim are lenient to allow one to continue learning past Alos, prior to saying Birchas Hatorah.
What is the law if one recited the blessing prior to Alos?
The blessing must be repeated after Alos. However there are Poskim that rule one is not to repeat the blessing a second time, and is rather to hear it from another person or have in mind to fulfill his obligation within prayer.
 Siddur; 47/7 [if no one is available]; and so rules: M”A 47/12; Elya Raba 47/9; Birkeiy Yosef 46/12; Mor Uketzia 47; Aruch Hashulchan 47/23; Kaf Hachaim 47/26; Soles Belula 47/4; Chayeh Adam 9/9; Derech Chaim; Mateh Yehuda 47/16; Ketzos Hashulchan 5/8; Birchas Habayis 34/8; Heishiv Moshe 2; Piskeiy Teshuvos 47/16.
Background from Shulchan Aruch 47/7:
If one was awake the entire night, according to the first opinion [mentioned in Background of previous Halacha] a blessing is not to be said in the morning, so long as one has not removed his mind from learning Torah. However according to the second opinion there which equates Birchas Hatorah to Birchas Hashachar, one is required to recite the blessing after Alos just as is the law with Birchas Hashachar, that the blessings are to be recited after Alos even if one did not receive their corresponding benefits.
Final ruling of Admur: In conclusion Admur in the Shulchan Aruch rules that one who desires to avoid doubt [of saying a blessing in vain], if possible, is to hear Birchas Hatorah from another person, having in mind to fulfill his obligation. Nevertheless, one who is unable to do so may say the blessing himself [as the custom is like the view mentioned above]. [ibid; and so rules Chayeh Adam ibid] Thus in the Shulchan Aruch Admur suspects for the first opinion, even though the second opinion is the main Halachic ruling. However in the Siddur, Admur plainly rules like the second opinion, that one may say the blessing himself, making no mention of the dissenting opinion. [Ketzos Hashulchan ibid; Glosses of R. Raskin on Siddur footnote 134] Hence according to the Siddur there is no need to hear the blessing from another person. [Shvil Hachaim 4/5; Piskeiy Teshuvos 47 footnote 135] Seemingly this is due to the fact that the Arizal held that Birchas Hatorah is to be recited even if one did not sleep at night. [Peri Eitz Chaim 4]
Other Opinions: The M”B 47/28 rules that one may not say the blessing himself and rather one is to hear the blessings from another person who slept, or is to have in mind to fulfill his obligation in Birchas Shema.
The law if one slept during the day a Shinas Keva: Rav Akiva Eiger rules that if one slept a set sleep during the day then according to all he is obligated to recite the blessing in the morning upon Alos. [M”B 47/28; See Levushei Mordechai 1/19] Likewise if one went to sleep in the morning after staying awake all night then he may recite the blessing after awakening according to all. [See Piskeiy Teshuvos 47/16]
 Shvil Hachaim 4/5; See previous footnote that this is disputed between the Siddur and Shulchan Aruch, and we rule like the Siddur. Vetzaruch Iyun why the Nesiv Hachaim [on the Derech Chaim 4/5] which brings instances that Admur argues on the Derech Chaim does not make mention of the fact that according to the Siddur one may say the blessing himself. Perhaps he learned that the Siddurs omittion of the dissenting opinion is not really a proof that Admur retracted his suspicion for the opinion in Shulchan Aruch. To note that in the Shevil Hachaim (by Rav Avraham Chaim Naah), which is a supplement to the Nesiv Hachaim, he does make note of this point that according to Admur one does not need to hear the blessing from another, however his proof is not from the Siddur but from the 59/4 which states that by the morning blessings one never fulfills his obligation through hearing another person saying them unless there is a Minyan present. This is a wonderment being that according to this view of 59/4, that it is also referring to the Torah blessing, there is an explicit contradiction between the ruling here in 47/7 and that in 59/4. Vetzaruch Iyun Gadol!
 Yair Hayom versus Alos: In the Siddur and Shulchan Aruch 47/7; 47/9 Admur uses the term Yair Hayom while in the Siddur regarding Birchas Hashachar the term “Alos” is used. Vetzaruch Iyun as to whether there is a difference between Yair Hayom and Alos. Seemingly there is no difference as Admur states that one may say the blessings starting from Alos [Siddur] and Yair Hayom [Siddur by Birchas Hatorah] and if there were a difference this would create a contradiction in Admur in the Siddur. Nevertheless it remains to be understood why Admur uses different terms each time. See glosses of Rav Raskin on Siddur p. 16 and 22
 See Chapter 8 Halacha 7; So rules also Halef Lecha Shlomo 33; Kaf Hachaim 47/29 [unlike his ruling in 46/49 regarding Birchas Hashachar that it may be said from midnight.]
 Piskeiy Teshuvos 47/16; Upashut!
 Kaf Hachaim 494/12; Ashel Avraham Butchach 46; Poskim brought in Piskeiy Teshuvos 47 footnote 139; and so rules Shevach Hamoadim [page 240] and Luach Kolel Chabad. So is clearly implied from Admur in Siddur that rules it is forbidden to learn prior to the blessing despite the fact that he rules Birchas Hatorah is like Birchas Hashachar. This clearly disputes the ruling of the Mahrshag and Rav Raskin brought in next footnote.
 Mahrshag 1/62; Minhag Yisrael Torah Hi 47/1; Poskim brought in Piskeiy Teshuvos 47 footnote 141; and so concludes Rav Raskin in his glosses on Siddur footnote 135 [however there are many questions on his explanation there as brought in previous footnote]; See Hiskashrus Shavuos and Sukkos which debates this matter.
 Kaf Hachaim 47/29; Piskeiy Teshuvos 47/16
 Kaf Hachaim 47/29; and so is implied from Admur in Siddur and 47/7 as according to all opinions prior to Alos he is not yet obligated to say the blessing and the first blessing was hence a blessing in vain.
 Bitzel Hachochma 5/168; Piskeiy Teshuvos 47/16 footnote 144