Being strongly cultural deterministic in my view of history, I think Africa's core problem laid in the cultures of the Bantu Peoples that expanded over much of its territory. Think about it: Even with more large domestic mammals and better metallurgy than the Americas and more diseases even than Eurasia, the Bantu-dominated Central and Southern portions of Africa were unable to organize into any large, assimilationist states, as nationalism (or "tribalism" as it is popularly yet erroneously known) was so strong that it crippled trade, communications and progress as a whole.
Have but a look at the Rwandan Genocide, the split of the Luba and Lunda Empires, the endless slave raids in most if not all of Precolonial Bantu Africa or the lack of the ability for, or will to, Bantu states to successfully assimilate conquered or otherwise subjugated peoples and ethnic minorities into their dominant culture.
Contrast this with one of of the most successful, advanced and enduring of all civilizations: China, now home to and overwhelmingly dominated by the largest nation in the history of humanity, the Han. And look at the similarities Bantu Africa has with Post-Classical Europe, with its ever-changing borders, its being the birthplace of two world wars and its love of the nation-state.
Besides non-Bantu Madagascar, the small creole-speaking state of São Tomé and Principé and Western-dominated South Africa or Namibia, the only truly successful country in Bantu Africa is Botswana: I strongly believe that its unique success among Bantu states is due to the fact that this is because the Tswana make up such an overwhelming majority.
The problem in Africa is analogous to, but far more severe than that of, the Balkans: Even when the Balkans were under a good and prosperous state - Tito's Yugoslavia - they ended up destroying it and their quality of life thanks to their inability to put aside their petty differences; and I can see no geographical disadvantages in the Balkans, neither those that were absent during the days of Pax Romana (or the time of the Hittites or the Classical Greeks...) nor those which put the Balkans at a disadvantage to Turkey, which is doing far better today. Now, replace the dozens of nations in the Balkans with the THOUSANDS in Bantu languages-speaking Africa, and it appears obvious why no real progress can be made until Bantu languages-speaking Africans are willing to give up nationalism.