seeming as Iran has transformed from a once modern and secular nation, into the Islamic republic we see today, I was wondering whether or not the Iranian revolution was started to establish an Islamic state, or was it more to do with getting rid of the monarchy?
Why it was an Islamic revolution? Some say it is because the Shah was able to systematically suppress non-religious opposition groups such as the various leftists and the communist party Tudeh and the clerical opposition is all that was left. (According to this theory religious opposition elements were tolerated because they were also anti-Communist.)
The secular Nationalists (the National Front) who were the heirs of Mossadegh did not have the same influence as the clerics among ordinary people as they tended to be Westernized upper-class intellectuals. But in reality the clerics in Iran have had a long history of political involvement and influence across the political spectrum. One of Mossadegh's biggest supporters was Ayatollah Kashani who was a member of the National Front, but he separated from Mossadegh after he became convinced that the Communists were gaining too much influence (the CIA's secret operations had a lot to do with this perception - they even bombed a cleric's house and blamed it on "Communists")
One can look further back the 1905 Constitutional Revolution in Iran, which was supposed to create a Constitutional Monarchy that copied the Belgian model but which included an advisory role for the clerics. Unfortunately that experiment which democracy was ended by joint Russian-British intrigue and the re-installment of the despised and corrupt Qajar, and later Pahlavi dynasty rulers. Clerics were also central figures back then in Iran too. There are more than a few books on this topic, ie
http://www.international.ucla.edu/cnes/event/11396
Some exile dissident groups (particularly the MKO) claim that Khomeini somehow "stole" the revolution from them but in reality Khomeini was the revolution and they were just hanging on to try to exploit it. The entire 1979 revolution was started by demonstrations occasioned by an anti-Khomeini letter that was published in a Tehran newspaper, and these demonstrations -- repeated every 40 days to mark the religious grieving ceremony for the deaths of protestors from the previous demonstrations -- eventually grew into the revolution. Khomeini's arrival in Tehran from exile in France, and later his funeral, are among the greatest gatherings of humans, ever.
Some of the other political factions tried to ride his coattails to power, hoping to later sideline him and his supporters but they were quickly and violently sidelined themselves. Among these the most glaring example is the MKO/MEK/NCRI (known by various pseudonyms) which was itself one of the most violent groups involved in the revolution, espousing a mixture of Marxism and Islam (often referred to as Iran's Khmer Rouge) and had assassinated Americans and supported the embassy hostage-taking but opposed the hostage release. They lost violent post-revolutionary battles with the Khomeini supporters, ran off to Iraq and started cooperation with Saddam against Iran during the Iran-Iraq war (and their members were mass executed in Iran, along with members of the old Communist party whose names had been provided to the Khomeini regime by the US as potential Soviet spies.)
{the MEK is still around. They "bought" their way off the US State Dept terrorist and were payng US politicians o support them quite regularly despite being listed as a terrorist organization https://www.theguardian.com/commentisfree/2012/sep/23/iran-usa Currently they're helping influence US foreign policy with respect to Iran too by hiring people like Rudy Guilliani as their spokesmen https://www.washingtonpost.com/news/josh-rogin/wp/2016/11/15/giuliani-was-paid-advocate-for-shady-iranian-dissident-group/ While they now claim to be secular and pro-democracy, historically even they had their clerical members who espoused Islamism mixed with Marxism }
So in a way it really isn't all that surprising that religious elements would be politically influential in Iran since 98% of Iranians are Shia moslems
As for the assumption in your question that Iran was "secular" and "modern" under the Shah:
Iran was not "secular" under the Shah, depending on how you define that term. The Constitution recognized Shiite Islam as the official religion and furthermore while the 1979 Islamic revolution did introduce many gender restrictive laws (such as the requirement for hair covering for women) various other gender restrictive laws were in place back then under the Shah too such as the law that prohibited women from traveling abroad without a husband's or father's permission. After all even the Shah had to respect popular religious sentiment and very occasionally would be shown praying at a mosque. Ostensibly women were legally equal to men in other areas, however because the average literacy rate for women was below 50%, these were nominal freedoms as most people were in fact too poor and backward to really have any say in govt anyway, assuming that it wasnt' an Absolute Monarchy in practice, and people were trying to just survive.
Iran was only "modern" during the Shah's time if you assume that literacy rates below 50% is "modern." In reality, back then most Iranians lived in rural settings too and Iran became very urban after the revolution. Iranians massively improved their living standards after the 1979 Islamic Revolution as shown by the UN's Human Development Index trends, at twice the rate of the rest of the world.
Only one other country (South Korea) was able to do better. http://www.ir.undp.org/content/iran/en/home/countryinfo.html
http://iranprimer.usip.org/blog/2013/apr/01/un-stats-life-longer-and-healthier-iran
Ironically it was many of the policies of the Islamic regime that actually empowered women there, for example massive improvement in education, family planning and healthcare:
http://www.reuters.com/article/us-iran-divorce-idUSKCN0IB0GQ20141022
http://www.latimes.com/world/population/la-fg-population-iran-20120729-html-htmlstory.html
Before the revolution, Iran's HDI was low and not at all rising.
This is how Iran changed after the revolution compared to other countries and the rest of hte world:
So in conclusion, Iran was really neither modern nor secular under the Shah, and the reason why it was an Islamic revolution is because clerical elements have had much greater influence and support among ordinary Iranians than other political actors who were either already discredited or too elite and lacked popular support.
The religious elements also had the revolutionary "infrastructure" of the various religious schools and mosques and where politics was discussed along with religious topics. In fact they regularly distributed cassette tape recordings of Khomeini's speeches while in exile too. The Shah had tried to undermine this religious establishment by for example promoting land reforms that were actually meant to deprive the religious organizations of their independent funding sources but that was not successful and only caused more resentment among the clerics.
The US Civil Rights movement is a good example to use here. When a people are oppressed and not allowed to develop public institutions to express their interests this function often reverts to the church. The Iranian people wanted to control their own government and the only national institution aside from the military was the church. The Islamic religion grew in Iran because the country was conquered by Islamists and in order for locals to participate in government they had to adopt Islam. So for Iranian nationalists to adopt Islam as the organizational basis for a national revolution repeated an older pattern and mirrored the structure that developed in the American Civil Rights movement.
