Everyone in the world has problems. That is part of the nature of life, and anyone living must encounter problems sometimes. Spiritual practice will not make anyone problem-free, despite what many people decide to believe.
Do people in an enlightened state still have problems? YES! If they have a body, they will encounter problems, and they will still require things like water, air, shelter, love and food. Living the most enlightened life possible might help you be healthier, but live long enough and eventually you will get sick. Eventually you will still die. You still have to find food, nourish relationships, keep warm, pay the bills - doesn't matter how much you meditate, your body has needs.
Though spiritual practice does not rid you of problems, it does help you cultivate better ways to deal with them, and cultivate the energy needed to deal with them. This may not sound like much, but actually this is huge! Learning how to BE with a problem.
Part of the issue is that people thing problems all start somewhere and have a beginning. Maybe they started when your girlfriend dumped you, or during your childhood, or whenever... But really - problems do not start at a certain point - they always exist. No matter how blessed your childhood was, you will have problems. Suffering begins long before childhood, and even before birth.
Of course, this doesnt mean that we shouldn't deal with difficulties! We must, and the more skillfully we do so, the better off we will be, and the better off those connected to us will be. But realizing that there is no end to problems and no end to suffering makes it easier to accept them and live with them.
When you mention "accepting" problems, people think this means you suppor them or repress them, but this is not the case! You can accept something and still address it and work to change it. Accepting it means that you do not deny it, and that you open yourself to all of life - not just positive things, but all things.
This is part of the key to non-dual awareness, and also to being your natural authentic self. If you accept the dark parts of yourself and your life, you are more able to change them. If you do not accept them, then you may fall into habits like repression or making drama.
An easy way to describe this is with the emotions. When you feel anger arise, you can accept it, recognize it, and let it go without it changing your behavior. But, if you try to deny it or resist it in any way, you give it attention and energy, and start an inner battle over your emotions. Accepting allows you to let go, fighting forces you to engage.
There are many ways to cultivate this skill - two of the most popular ways being meditation, and working with entheogens. In meditation, you work on cultivating awareness and acceptance and letting go daily practice. With entheogens, the spirit of the plant shows you what you are hiding from, and allows you to accept it and integrate it into your life consciously and responsibly. Both paths can lead to similar results when practiced correctly.