There were three campaigns by Nebuchadnezzar against Jerusalem:
605 BC (Dan 1:1-3), when the prophet Daniel and a host of the Judean nobility was taken captive and deported. At this time, the Judean kings effectively lost their Independence and because of their rebellion, we later punished by Nebuchadnezzar.
597 BC Jehoichin and Ezekiel taken captive
586 BC - final destruction of Jerusalem and the temple during the final year of Zedekiah. Jerusalem was not immediately abandoned but less than a year later, Gedaliah was assassinated and the remaining Jews who fled to Egypt.
There are actually three distinct 70 year prophecies in the Bible:
70 Years of Isaiah
Isa 23:15, 17, predicts that the city of Tyre would be “forgotten” for 70 years after which, it would return to its previous “promiscuous” way. The known history of Tyre can be stated briefly as: Nebuchadnezzar began a 13-year siege of Tyre in about 575 BC which ended in about 562 BC but Tyre resumed its sovereignty soon after Cyrus became sole ruler of Persia (about 537 BC). It was again captured and destroyed by Alexander in 332 BC. In 315 BC the city was again placed under siege by the Macedonian general Antigonus and captured the following year. In 126 BC Tyre gained its independence from the Seleucid Empire but became a Roman province in 64 BC.
Isa 23:15 specifically makes this 70-year period “the span of a king” – that of the duration of the Babylonian empire. During the Babylonian domination period, Tyre was conquered and became a minor city. Following the collapse of Babylon, Tyre was made a satrapy in the Medo-Persian Empire. Thus, Isa 23 is part of a series of prophecies about how Babylon would dominate the whole area, including (in this case) Tyre.
70 Years of Jeremiah
There are two prophecies of Jeremiah which are possibly the same prophecy. Both Jer 25:11, 12 and Jer 29:10 predict that Judah would serve the king of Babylon for 70 years, during which the land would become waste. This was fulfilled beginning in 605 BC when Nebuchadnezzar captured many of the nobility in the first Judean campaign. Two more campaigns followed in 597 BC (where another 10,000 captives were taken), and the final in 586 BC that destroyed the city. In Oct 539 BC Cyrus defeated the Babylonian kingdom. His first regnal year began in Sep 538 BC and he issued the decree recorded in Ezra 1 in early 537 BC. It was also during this first regnal year that Daniel 9 is recorded and refers directly to the prophecies of Jeremiah and the 70 years. The decree went into effect when the Jews organised themselves and departed Babylon (Ezra 1) probably in 536 BC, 70 years (by inclusive reckoning) after the first captivity of Judah.
2 Chron 36:21 also quotes Jeremiah’s 70 years and says that “the land enjoyed its Sabbath rests all the time of its desolation.” This suggests that the 70 years was to make up for previous years when the 7th year of Sabbath rest was not observed making a total of about 490 previous years – about the total time of the Israelite monarchy from Saul to Zedekiah.
Daniel 9:2 also refers to Jeremiah’s 70 years of captivity. In Dan 9:2, Daniel says that the 70 years would be the duration of the city’s “desolation”, a reference to the fact that Jews had been held captive by Babylon for almost 70 years. The subsequent prophecy in Daniel 9:24-27 is couched in terms that are seven times greater than the 70 years of Jeremiah.
70 Years of Zechariah
Zechariah 1:12 & 7:5 appears to allude to another 70 years during which the temple remained unbuilt. Nebuchadnezzar destroyed the temple in 586 BC, and later, Zerubbabel and Haggai supervised the completion and rededication in 515 BC, about 70 years later, in the second year of Darius, Zech 1:1, 7, or perhaps the fourth year, Zech 7:1.
Thus, Daniel appears to date his 70 years "desolation" of Jerusalem from his own capture and deportation to Babylon in the "the third year of the reign of Jehoiakim king of Judah", Dan 1:1.