Does God really care about our problems?

Nope. 

4.8 million children under age 5 died of starvation and disease last year, the trend continues this year,  just as it is EVERY year; so what do you think....their parents didn't believe?

There's no way to really know.

Nope

Even if I believed in a god … which I don't … the evidence is pretty clear that god doesn't care about us., due to all the suffering in the world.

Even if you claim the suffering is the result of "free will" … that still means god doesn't care about those who actually need his protection - those who are too weak to protect themselves.

Yes! God truly cares about our problems. Notice the comforting assurance in these scriptures: “Humble yourselves, therefore, under the mighty hand of God, so that he may exalt you in due time, while you throw all your anxiety (cares; worries) on him, because he cares for you.” (1 Peter 5:6, 7) The psalmist sang: “Jehovah is giving support to all who are falling, and is raising up all who are bowed down.” (Psalm 145:14) We should believe these assurances, for they are found in God’s Word.  One thing is sure: Faith in God and his Word promotes spiritual well-being because it strengthens our conviction that he really cares about us.

Here's my take on it, but it's only an opinion.

Let's suppose for a minute that there is a god out there. Even though the various religions personalise him in various ways, do you really think that the being that created the Universe can take a personal interest in the day-to-day existence of every creature on one rather insignificant planet? He'd go stark, staring bonkers inside a week.

Such a god would set various systems in motion (we call them the laws of nature) and allow the sentient beings he created to interact with them as best they could.

So if you put your hand into a flame you'll feel pain;  if you develop an attitude that puts you in conflict with other people you'll face the consequences. Then there are all the chance things that can happen to us, and the hereditary things (the genes of the father may well be visited upon the child). Other problems -- like the starvation that plagues many countries -- are also created by people, through  the mismanagement of resources.

But it's inappropriate to blame "God" for our problems. They're just a part of life. Basically they won't go away unless we stand up, face them, and force them back.

It was a wise mind that first said, "God helps those who help themselves."

God really cares about us and in the Bible he has promised to remove all causes of suffering at Psalm 37:9-11," For evil men will be done away with. But those hoping in Jehovah will possess the earth. Just a little while while longer the wicked will be no more. You will look at where they were. And they will not be there. But the meek will possess the earth. And they will find exquisite delight in the abundance of peace."  What a wonderful future God has for all obedient ones.