What problems confronted Roman Republic by 78bc?
I’m assuming you mean in a reasonable timeframe around 78BCE. There were several problems that faced Rome, there were two servile wars, the biggest being in Sicily. There was a problem with the Allies of Rome and the Italians, which brought about the Social War, but most significant in this time period was the rise of the powerful generals, most notably Marius and Sulla, which thrust Rome into civil war. Sulla was the ultimate victor of this war and was made dictator to fix Rome’s more serious problems. Sulla died in 78BCE and this is the typical starting point for those that are studying the Fall of the Roman Republic. (Unless they want to start with the Gracchi in 133, but that makes for a long study) This is but a superficial answer, the headings of the topics, written as a guide for you to look into further; for understanding will come only through further reading. A proper answer to that question cannot be attempted through this medium.