Gemara

(Rav Yehudah): "Al Mah Ovdah ha'Aretz" (why did the Churban come)? "Mi ha'Ish he'Chacham" (Chachamim could not answer) "va'Asher Diber Pi Hash-m Elav" (the prophets could not answer), until "va'Yomer Hash-m Al Azvam Es Torasi Asher Nosati Lifneihem" (Hash-m explained, because they abandoned My Torah).

(Rav Yehudah): They did not bless before learning.

Berachos 11b (Rav Yehudah): If one wakes up to learn before saying Keri'as Shema, he must bless (Birkas ha'Torah); if he already said Keri'as Shema, he does not bless, for Ahavah Rabah exempts him.

(Rav Huna): One must bless for learning Mikra (Torah, Nevi'im or Kesuvim), but not for Midrash.

Rishonim

Question: If one rises early and says requests, verses or Tehilim until dawn, must he say Birkas ha'Torah beforehand?

Answer (Rambam, Pe'er ha'Dor 104; 25 in some versions): Always, one must say Birkas ha'Torah before verses, even one verse. We do not distinguish whether it is in the way of supplication.

Rosh (Berachos 1:13): If one rose early to learn before going to the Beis ha'Keneses and blessed Birkas ha'Torah, he does not bless again when saying the Korbanos in the Beis ha'Keneses.

Rosh (Teshuvah 4:1): If one rises early to learn, he blesses all the Berachos until and including Birkas ha'Torah.

Poskim

Shulchan Aruch (OC 46:9): One may not say verses before Birkas ha'Torah, even in the way of supplication. Some say that one need not be concerned, since he says them in the way of supplication. It is good to be concerned for the first opinion.

Rema: The custom is like the latter opinion, for during the days of Slichos we say Slichos, and afterwards Birkas ha'Torah with the other Berachos. Also every day we say verses and supplication when entering the Beis ha'Keneses, and afterwards Birkas ha'Torah. Our custom is to say Birkas ha'Torah right after Asher Yotzar. One should not deviate.

Tur: R. Yehudah ha'Chasid would say Kri'as Shema in Korbanos... and Birkas ha'Torah before Parshas ha'Tamid. I found this difficult, for there are verses beforehand! I said it immediately after Elokai Neshamah. I saw that Sidur Rav Amram Gaon puts it after Eizehu Mekoman and the Beraisa of R. Yishmael's 13 Midos.

Prishah (29): He means that Rav Amram Gaon put Ribon ha'Olamim (and Kri'as Shema)... after Eizehu Mekoman, to avoid verses before Birkas ha'Torah.

Magen Avraham (15, citing Levush (581:1): Only Ashkenazim, who normally say Birkas ha'Torah after (some texts - before) Parshas ha'Tamid, permit verses before Birkas ha'Torah. We who say it right after Asher Yotzar must say Birkas ha'Torah beforehand.

Magen Avraham (6:7): The Darchei Moshe and Maharil conducted like the Sefardi custom to bless beforehand. However, a Shali'ach Tzibur without said it at home may not repeat it for the Tzibur, for everyone knows Birkas ha'Torah and says it for himself.

Beis Yosef (DH v'Huksheh): The Agur says that Birkas ha'Torah is only when one intends to learn, but not for verses said like supplication. The Ra'avad and Maharil require Birkas ha'Torah also for this, but in a Teshuvah the Maharil said like the Agur. Orchos Chayim says that when we say Slichos before dawn, we say Birkas ha'Torah and learn a Halachah, a Mishnah of Eizehu Mekomam or another Mishnah, and afterwards Ashrei, for one must bless on Tanach.

Mishnah Berurah (27): Since our custom is to say Birkas ha'Torah right after Asher Yotzar, we hold that one may not say verses even in the way of supplication beforehand. The same applies during Slichos.

Kaf ha'Chayim (55): The Shulchan Aruch is stringent, like like the Rambam, Ra'avad, Orchos Chayim, Tur and Maharil.

Kaf ha'Chayim (56): One need not bless for a words of a verse said merely for a nice expression. The Shulchan Aruch (YD 284) similarly permits writing words of a verse without Sirtut if it is cited merely for a nice expression.

Kaf ha'Chayim (57, 4:16, 8:6, 25:68): Also the following should not be said before Birkas ha'Torah: "va'Ani b'Rov Chasdecha" upon entering the Beis ha'Keneses, "Se'u Yedeichem Kodesh" when lifting his hands after washing them in the morning (unlike Sidur Ya'avetz), "Borchi Nafshi..." when putting on the Talis, and "va'Aristich Li Le'olam..." when winding the Tefilin strap around his finger.

Birkei Yosef (46:16): One who says "Vihi No'am" before every Mitzvah should not do so before Birkas ha'Torah.

Maharshal (Teshuvah 56): Early Sidurim put Birkas ha'Torah before Parshas ha'Tamid. The Tur changed the previous custom needlessly. Do not say that he is merely stringent to require Birkas ha'Torah before verses said in the way of supplication. If so, also Birkas Kohanim does not require Birkas ha'Torah. If so, his Berachah is Levatalah, for there is a large interruption before ha'Tamid! The Rosh and Tur require learning immediately after Birkas ha'Torah, unlike the Mordechai.

Yabi'a Omer (4 OC 7:1): Tosfos, R. Yonah and the Mordechai obligate learning immediately afterwards only if he wants to be Yotzei through Ahavah Rabah, but not if he says Birkas ha'Torah. This is unlike Berachos on food, for one is obligated to engage in Torah constantly. Therefore, an interruption does not disqualify the Berachah. Acharonim say that the Berachah takes effect on Birkas Kohanim, for we say it in the way of learning. The Maharshal holds that it is conciliation and Berachah.

Yabi'a Omer (ibid. DH v'HAlom): If one is in Pesukei d'Zimrah and realized that he did not say Birkas ha'Torah, Shulchan Melachim says that he says it between Yishtabach and Yotzer Ohr. Seemingly, one may not continue Pesukei d'Zimrah until saying it! If he holds like those who permit verses in the way of supplication, this does not permit "va'Yvarech David" and Shiras ha'Yam! (We say them on Tish'ah b'Av because they are part of Seder ha'Yom, like Parshas ha'Tamid and Eizehu Mekomam.) I say that he should immediately bless Asher Bochar Banu. This permits to say the rest of Pesukei d'Zimrah, and between Yishtabach and Yotzer Ohr he says the other two Berachos, Asher Kideshanu and v'Ha'arev Na. This is not an interruption (in Pesukei d'Zimrah), for it is necessary, like interrupting between a Berachah on food and eating to say 'prepare food for the ox' (Berachos 40a).

Yabi'a Omer (ibid. 3,6): The Mechaber brought two opinions, and concluded that one should be concerned for the first opinion. It was not a clearcut ruling; it is proper to be concerned for the first opinion. Usually, when he brings an opinion, and 'some say...', the Halachah follows the first opinion. Here is different, for his final words show that it is a mere stringency. Chikrei Lev and Aruch ha'Shulchan say so, unlike the Birkei Yosef. When necessarily, one may be lenient, e.g. to answer to Kedushah before Birkas ha'Torah. Also, She'alas Ya'avetz (81) holds that the Isur to say verses by heart refers only to full verses. Perhaps here also, the Isur is only for full verses (in answering Kedushah, the only full verse is "Yimloch..."). However, some argue with the Ya'avetz, and perhaps here is different.