Posting on mobile, so please forgive any typos:
Short answer:
the Qing were so assured of Chinese superiority that they found it difficult to conceive of foreign or 'barbarian' ideas and technologies being useful
the imperial examination system used by the Qing to select high officials encouraged essentially conservative thinking that reduced the likelihood that Qing officials could successfully propose reforms to industrialise
when the court began to accept the need for modernisation in the 1850s and 1860s, it was purely focused on military modernisation and failed to recognise that industrial societies thrived with healthy competition and trade, rigorous education systems, and civil societies. Thus, modernisation was half hearted at best.
due to internal rebellions and growing Han Chinese nationalism, the Qing grew increasingly reactionary and even more conservative by the 1880s and 1890s. For example, the Guangxu Emperor's 1898 reform program (which intended to emulate the Meiji Restoration in Japan) was ended by a palace coup instigated by reactionary princes and the Dowager Empress Cixi. When Cixi finally permitted reforms to go ahead 3 years later, it was too late: the New Government reforms which sought to create a modern industrial society simply accelerated the collapse of China, as the reforms created a discontented civil society capable of demanding the Qing's overthrow before they had time time to create an industrial base needed to strengthen the Qing regime and thereby give it legitimacy in the eyes of Han Chinese elites
Long answer:
Let's start with China's first substantive contact with the industrialised western world: the Macartney mission. A British diplomatic mission is dispatched in 1793 led by Lord George Macartney sought to persuade the Qianlong Emperor to open Chinese ports to British merchants. Macartney brought rich trade goods showing off the mastery of early industrial Britain - such as mechanical clocks. However, Qianlong had the good fortune to reign over a stable and prosperous empire in a time of great wealth, and interpreted the British gifts as tribute from an inferior state - the same that he might collect from a Mongol prince or a Korean king.
Had the Qianlong Emperor permitted greater trade, perhaps European industrial technologies might have made slow inroads into China. Instead, his memorial of reply addressed to King George III shows us that his government literally could not imagine needing any non Chinese commodity or technology: "Our Celestial Empire possesses all things in prolific abundance and lacks no product within its borders. There was therefore no need to import the manufactures of outside barbarians in exchange for our own produce. But as the tea, silk, and porcelain which the Celestial Empire produces are absolute necessities to European nations and to yourselves, we have permitted, as a signal mark of favour, that foreign hongs should be established atCanton, so that your wants might be supplied and your country thus participate in our beneficence."
It's worth stopping here to explain the hong system, as it helps explain the slow spread of industrial technology. Under the Qing, foreign trade was carefully regulated, with Westerners only being permitted to trade with a handful of licensed corporations (hongs) in Guangzhou (Canton, as it was known to the English). This limited the entry of industrial technology to a single port in the south, far removed from the centre of imperial government in the north in Beijing. Furthermore, Chinese trade regulations were designed to prevent a deficit of silver. Since silver was the basis of the currency and taxation systems, any deficit in the supply of silver would cause inflation. Therefore, all Chinese exports had to be paid for by Europeans in cash - reducing further the likelihood of European merchants introducing new technologies to China. So, a system of trade designed by the Qing to ensure financial stability had the unintended effect of insulating China from the introduction of industrial technologies.
So China under the Qing was initially convinced of its superiority in all things and had no need of industrial technology, and insulated itself from the spread of these technologies through its trade regulations. This means western industrial technology could only be introduced to China by war, rather than by trade. Therefore, the Qing were always going to be playing a game of technological catch up.
That brings us to the First Opium War of 1839-42. An imperial commissioner, Lin Zexu, gave the order to confiscate and destroy British merchants' stocks of the addictive drug opium. The British government used this as a pretext for war, which conveniently allow them to force open Chinese ports open to trade and end their reliance on silver to trade with China. British ironclad steamships easily defeated Chinese wooden and sail powered warships and bombarded forts around Guangzhou , and British marines with modern rifles easily overwhelmed the Chinese garrison. Here, surely, the value of industrialisation would become clear?
Well, yes and no. Some progressive elements of the state bureaucracy began to endorse adopting western industrial technology though the Self-Strengthening Movement in the 1850s and 1860s. Their case was reinforced by subsequent instances of gunboat diplomacy by Europeans and the outbreak of the Taiping Rebellions, a massive conflict which could not be contained the Qing's peacetime standing armies, the Eight Banners. But the impetus for reform was constrained by the essentially conservative character of the Chinese bureaucracy and court. The imperial examination system, which was used to select candidates for high office, was based on mastery of Confucian philosophy as outlined in classical Chinese texts. This bred a conservative, sinocentric worldview that convinced officials that Chinese civilisation was superior to that of the barbarian societies around it, and Confucian tradition provided a bedrock of stability that helped weld together the disparate peoples of the empire. The officials who wrote memorials to the Emperor advocating Self-Strengthening were therefore careful to confine their recommendations to adopting barbarian weapons - and not any of the other ideas or technologies of a barbarian society. The theory was that western guns could defend a Confucian political order without in any way modifying its constituent elements. But any student of the industrial revolution will point to the diverse requirements of successful industrialisation: intellectual property rights that reward innovators; private property protections and civil rights that protect innovators from arbitrary government interference; education systems that promote liberal arts and scientific method in order to enable a culture of experimentation and innovation; banking systems to provide credit to worthy innovators. Thus, the Self-Strengthening Movement did bring highly limited industrialisation to China - but Chinese armouries and foundries always used technology that was a generation behind that of Europe as there was no indigenous innovation going on. So Chinese guns and warships would generally speaking be a generation behind the Europeans they were fighting.
It's worth noting that Japan did not suffer from the same problem. The Meiji Restoration was a much more all encompassing modernisation program: Japan didn't just try to build modern guns and a modern army; it also developed a modern banking system, railway network and education system, promoted free trade and innovation, and thereby encouraged indigenous and meaningful industrial growth. Hence, Japan came to possess many of the features of a Western industrial society by the late 1800s.
Main source thus far: Immanuel Hsu's doorstopper The Rise of Modern China, sixth edition
(Will continue discussing failure of reforms and sources tonight).