I note that you added a caveat of "significant" as a qualifier before the word invention. The use of a vague adjective is deliberate because you know that scientific inventions were present during the Ottomon and Mughal years, you just don't want to give them any credit. Therefore, I don't think it would be wise to provide any examples (a simple google search brings up many), because you will simply dismiss them as non-significant, since obviously you have no interest in looking at this objectively, but rather scoring points.
That brings us to the second point. Universities in pre-Islamic India. Sure there were a few, and like any normal civilization that exists and progresses, centers of education were a must. Nalanda, the most famous one, was a Buddhist center of learning. Taxila and Vikramshila, two other famous ones, were also Buddhist Universities. There were also few less famous one, whose names escape me now, but they were all Buddhist centers of learning.
I am quite perplexed that why did the Hindus not establish great centers of learning? Could it be because of the infamous caste system, where education was reserved for only the Brahmin class? Is it possible that in order to get educated, ancient Indians converted to Buddhism, in order to access education? And perhaps that is why these universities flourished?
You then go on to make the claim that the Muslim empires in India, provided patronage to the madrassas, where scientific invention was scarce, and that is what contributed to the eventual colonization of India.
These are very tall claims that take an element of truth and surround it by lies to further a weak position. While it is true that madrassas were patronized by the ruling Muslims, these were not religious seminaries as they are today. During the Muslim world, madrassas were schools where every science was thought. Education was imparted to both Muslims and non-Muslims. The famous pearls of Akbar's court, all Hindus, were all educated in madrassas.
Like every education system, when closely analyzed, flaws begin to appear. This was no exception. Modern historians have noted some of these flaws, namely that education was stale and narrow. Basically a curriculum once established, was rarely modified to meet the evolving needs of society.
Now I am sure we can say that this was one of the contributors of British rule in the subcontinent, but to claim that this was the only contributor or even a major contributor is a stretch.
