The 1800s saw a huge number of problems in China, particularly in South China. There were numerous famines (1810, 1811, 1846, 1849), a good bit of piracy on the Southern Coast, plus you had the Opium War (1839-1842) and, starting slightly before the Taiping Civil War, you had the Punti-Hakka Clan Wars (from about 1855 to 1867, and, fun fact, being fought at the time on the Malay Peninsula as well). Then before the Taiping Civil war was over, you had the start and end of the Arrow War, a.k.a. Second Opium War.
In addition to all of this (because it clearly isn't enough), you had major economic hardships in the south (which were in large part the thing that set off the Punti-Hakka wars, but certainly not the only thing being fought about) as a result of urban centres exceeding the carrying capacity of the land and as a result of that, large scale migrations throughout the region.
In addition to all of that, at the same time you also had the Nian Rebellion from 1851 to 1868, catastrophic flooding of the Yellow River in 1851 and 1855, which devastated the grain supplies for the country and killed countless people.
Then in the South you had racial/ethnic animosities, not just directed toward the Manchu-run Qing, which was seen by many as illegitimate, but internally as well, between Hakka, Hoklo and Cantonese. Animosity between these groups was long-running and, as mentioned, not restricted to China's political borders.
Add to that the prolific secret societies (from which the Triads, the co-called "Chinese Mafia" got it's start in the 20th centuries) which had developed self-styled anti-Qing origin stories (some more legitimate than others) and from whom Hong Xiuquan's march north got support.
People were angry and a large number surely felt helpless. There was not enough food, not enough work opportunities at home. By the beginning of the Civil War, over 20,000 men from South China, almost exclusively from the Pearl River Delta area, had decided that heading to California and living in terrible conditions in a country that didn't particularly care for their well-being doing back-breaking labour (for substantially less than what white were making) was still a much better deal than staying at home with their families. It's precisely the same issues prompting the start of the Taiping Civil War that also prompted the largest influx of Chinese migrant workers into places like California.
It's not that Hong Xiuquan was so convincing. It was that he was an alternative to a really bad situation and someone in whom people could put their hope. It's a wonder it didn't completely topple the Qing, and while we don't really like to speculate here, there's been a good bit of writing that had the Arrow War not gone as it had, specifically in terms of British actions, they might very well have done just that.
tl;dr: People were pissed off and super desperate. The 1850s were not a good time to be a poor Chinese peasant, not that many times are.
Selected Further Reading:
Platt, Stephen R. (2012) Autumn in the Heavenly Kingdom —— Taiping-specific, a good read and gets into some of the speculative stuff, albeit appropriately briefly.
Erbaugh, Mary S. (1992) The Secret History of the Hakkas: The Chinese Revolution As A Hakka Enterprise The China Quarterly —— Talks a little bit about the role secret societies played in the northern march and the Taiping endeavour more generally
Leong, Sow-Theng (1997) Migration and Ethnicity in Chinese History —— Talks in great detail about all of the issues regarding economic and agricultural issues going on in the period