I think the Republic went wrong when Caesar was outlawed, some Tribunes had a track record of corruption, but Mark Antony looking out for Caesar's interests doesn't mean he wasn't also concerned about the people. The same goes for other "corrupt" Tribunes.

I also think it is worth questioning the theory of wealth and power destroying the Republic, because there was plenty of late republican development that was clearly beneficial, Citizenship was granted to Italy, more allies elsewere, in contrast to the Dominate corruption trials and trials for offenses like bribery happened regularly enough so there had to have been at least some deterrent for those without any connection to Cicero, Hortensius and other top orators, the status of women improved to a level that wasn't seen again untill relatively recently, the Roman State began giving cheaper bread and housing to the poor, I could go on.

In the end whatever the shortcomings, however wealthy ambitious men used their money to undermine it's democratic value, or how much the Tribunes slept on the job the only way for the Republic to fall was through a civil war involving armies.

The best conclusion I think is the Senate just didn't have a plan for keeping the loyalty of the new armies of the late republic, and as a result it collapsed, like any government that raises an unlimited number of soldiers without bothering to make sure they would serve the government. It may sound rediculous, but take a look at all of the horrible governments in the world today that make the Roman Republic seem saintly, none of those ever collapse so I'm not convinced the Republic collapsed for those reasons.