I think the problem is that the masses, most notably those below the poverty line, are demoralized. The problem runs so deep that every Filipino's mindset is stuck at "getting ahead first" instead of "helping each other to get there." In other words, everyone's just looking out for his/her own ass.
This mentality is also what's prompting many of the Philippines' citizens to vote for leaders promising to end their poverty - which is pretty sick, since any leader with the right intentions would be smart enough not to make such a big promise.
Can one leader solve it all? I highly doubt it. The poverty cycle usually takes around 2 generations to break, so real change will probably only happen in the next 50 years or so. Magsaysay was on the right track, but it only takes a few idiots to ruin the great work of hundreds. Those in power will always be tainted with corruption, but when a whole country's citizens are infected with it like a cancer, therein lies the real problem.