The prophecy of Daniel 4 was regarding Nebuchadnezzar. It is a Protestant tradition to try to give prophecies second fulfilments in order to try to give them meaning for the people of their times. As the centuries move on, so do the interpretations of these second fulfilments.
I am sure there have been many other interpretations of Daniel 4, but pertaining to where Russell got his interpretation from I have found the following.
In 1823 John Aquila Brown published in The Even-Tide that the "seven times" of Daniel 4 were prophetic of 2520 years running from the beginning of Nebuchadnezzar's reign in 604 B.C. to 1917 A.D. He did not equate this to the end of the Gentile Times.
In the 1830's a farmer named William Miller explained that a number of prophecies were to conclude in 1843, and so came to the conclusion that Daniel 4 was also to end in 1843. To do so he claimed the seven times started when Manasseh was taken as a captive to Babylon in 677 B.C. This was to signify the 'time of the end', the destruction of Babylon and when the dead would be raised. Apollos Hale and Sylvester Bliss corrected this date by removing the year zero that Miller had used in the calculation, promoting the time of the end to the year 1844. At Miller's suggestion Samuel Snow calculated that the end would arrive on October 22. This was to correspond with the tenth day of the seventh Jewish month, the Day of Atonement for the year 1844. Rather than using the current Jewish calendar he used an older calendar invented by the Karaite Jews. Jehovah's Witnesses still use the Karaite calendar in their calculations, including for the date of the memorial.
When 1844 proved to be false prophecy it was reworked by Second Adventists, such as Barbour to move the start date to 606 B.C. and the end date to 1914 A.D. Russell took his teaching directly from Barbour.
This was expected to culminate in Armageddon. With the failure for the end to eventuate in 1914 most Adventist groups came to recognise that Daniel 4 was not intended to have a second prophetic fulfilment and stopped referring to it.
It wasn't until the 1940's that the Watchtower Society officially removed the zero from their calculations. In order to retain 1914 they changed the desolation of Jerusalem from 606 B.C. to 607 B.C.
