Can democratic government solve the problems of today?
While democratic government may be able to solve some problems, there is no one-size-fits-all solution to all possible problems one could imagine. Even more importantly, some things which may be considered problems by some people are not considered problems by other people.
For example, while many people consider gender inequality a problem, and would note that liberal democracies have tended to be more successful at promoting gender equality than many more autocratic regimes, other people are opposed to gender equality. Also, there is no absolute proof that gender equality is incompatible with illiberal regimes.
On issues of global climate change and environmental degradation, some liberal democracies have taken leadership roles in reducing carbon emissions and other forms of environmental protection, but China, which has a centralized and authoritarian regime is also moving towards renewable energy and starting to tackle pollution and other environmental issues.
While many people view freedom and democracy as inherently valuable, others do not, and thus one can only speak of lack of freedom as a problem within certain cultural and ethical contexts.