I agree with you on one point: Our world does face a multitude of problems that seem almost unsolvable. But that should make us pray more, not less! We can't solve our problems on our own; we need God's help, and that's why we should pray.
I hope you'll stop and think about what you've written. What you're really saying is that God doesn't care what goes on in the world -- or if He does care, He can't do anything about it. But this isn't true. From one end of the Bible to the other we discover that God not only made us, but He deeply cares what happens to us. Evil is real, and so is human suffering. But God hasn't abandoned us -- and the proof is that He sent His only Son into the world to bring us back to Himself.
And God also intervenes in human affairs -- even when we don't realize it. The Bible says, "Surely the arm of the Lord is not too short to save, nor his ear too dull to hear" (Isaiah 59:1). He responds as well to the prayers of His people -- which is why the Bible commands us to pray for our leaders (see 1 Timothy 2:1-4). How much worse would our world be if people didn't pray?
I urge you to face your own need of God, and humbly open your heart and life to Jesus Christ. Then pray for our leaders, that they'll have God's wisdom to deal with our problems.