I wrote a paper on the independence movement of Albania for a university class last year, so I may be able to give some insight. It mostly covered the period from about 1870 to 1912, but I did some reading on medieval Albania as well.
The Albanians are not ethnically related to any other group in the region, at least not closely. There were two main ethnic groups within Albania, Gegs in the north, Tosks in the south. Prior to the Ottoman Empire, the Gegs were mostly Catholic, while the Tosks were primarily Orthodox. They were a very tribal society, with strong connections to your clan and region.
The Turks first invaded in the 1440's, but faced opposition in the figure of George Kastrioti, a local chieftan. He managed to halt the invasion until his death in 1468; Albania was conquered shortly after. In recognition of his efforts, the Turks referred to Kastrioti as "Skanderberg," in reference to Alexander the Great, and he is now regarded as the Albanian national hero.
As Albanian culture was tribal in nature and unlike neighbouring regions, they acted unlike the Greeks or Serbs when conquered. It was Albanian custom to always carry a weapon on their person, and the only people allowed to within the Ottoman Empire to do this were Muslims. So Albanians almost en mass converted; they also did this because there was animosity with the Slavic groups around them, and by becoming Muslim they ensured protection from the Turks. Even so, many Albanians didn't really care much about their religion; it was not uncommon for them to have both a Muslim and Christian name, and it also meant that unlike the still-Christian peoples of the Balkans, the Albanians never developed a national identity through their religion.
As one of the few European peoples to convert, the Albanians gained the favour of the Ottoman, and were allowed to pursue positions of power within the empire. Their traditional way of life was largely unaffected while ruled by the Ottoman, as the chieftan system was so entrenched within Albania. And nearly 20% of all Grand Viziers (prime minister, for lack of a better word) of the Empire were ethnic Albanians, by far the largest non-Turkish group.
Because of this, there was no serious call for an independent Albania, or desire to assert their ethnicity. They were quite content to remain within the Empire. This though was also aided because Albania is a very remote, mountainous country, and there was little development made within it during the 400 years it was part of the Ottoman Empire. There was also no writing system developed for the Albanian language, so communication was almost impossible amongst large distances.
Only in 1878 did an independence movement begin amongst the Albanians. The Turks had lost the Russo-Turkish War of 1877-78 that year, and the resulting Treaty of San Stefano called for large parts of Albanian territory to be ruled by various Slavic states. As the Albanians were quite opposed to this, and wanted to remain part of the Empire, they began to create a national movement. But since the Great Powers didn't want Russia to have to much influence in the Balkans, the Conference of Berlin was held and decided to modify the territories of the Balkans. An Albanian delegation went to the conference to ask that their land be kept within the Empire, but were rebuffed; Bismarck even said that an "Albanian nation simply did not and could not exist." The Great Powers agreed to split up the Albanian territory.
This led to an uprising in Albania, which forced the Sultan to reluctantly attack his most loyal subjects and get them to agree to the terms of the Conference. This only further solidified the Albanian people.
At this point they finally began working on creating a writing system for Albanian. Various groups proposed using Latin, Cyrillic and Arabic scripts, but disagreements meant that it was not until 1908 that a Latin alphabet was created. It was chosen in part to keep it distinct from the Arabic-based script used to write Ottoman Turkish.
Even with their movement gaining support amongst the people, most Albanians still wanted to remain part of the Empire, though an autonomous part. They realised that an independent Albania would be weak and likely to be invaded by neighbouring states, so they kept asking the Turks to make this happen. This changed with the Young Turk revolution in 1906. As ardent Turkish nationalists, they tried to suppress Albanian nationalism, and wanted a more centralised government, which went against the Albanian goals. Revolts became common within Albania, and a series of wars with neighbouring states made Turkey weak. The final one was the First Balkan War of 1912.
As a result of these wars, Albania declared independence on November 28, 1912, which was confirmed by the Great Powers during the treaty negotiations ending the Balkan War. That created the modern state of Albania, which only wanted out of the Empire as it realised they were no longer safe within its borders