There are a few points I'd like to out forward to you.
First, each one of us has a responsibility and some choose to fulfil their responsibilities while others choose not to. Our main responsibilities as Muslims is to act according to the command of Allah in every part of our life. This does not mean that if I pray then I must be rich for example. We are not doing a favour to Allah by praying or fasting rather it is a favour on us because we are able to stay far from a life of degradation where in the midst of enjoying every physical pleasure on earth, the soul feels empty and dead from a spiritual life. There is more I can write to you about this but I am giving you brief answers to make it easier.
Secondly problems come to everyone in different times of their lives. That does not mean that Allah is ignoring you. If problems mean Allah is ignoring you, then what about Imam Hussain. Does the day of Ashura and the captivity of the Ahlulbayt mean that Allah ignored them? No! When ibn Ziyad told Hazrat Zainab 'Do you see what Allah has done to you?' to which she replied 'I do not see anything but beauty' and this is after seeing her brother's brutal martyrdom. Her statement has many secrets.
Thirdly If the problem is a test as you say then you should be proud Allah has chosen you to test and if it is a punishment then you should be thankful that Allah is wiping out your sins so you have a clean plate and can go closer to him.
Fourthly the actions of a particular person or community cannot be blamed on Allah or his laws.
We need to look at our problems from a clearer lens so we can find solutions to our problems.
I would recommended you choose a particular Dua or amaal and focus on that for attaining connection to Allah and don't try and read all the duas in the books because that will make you tired and the connection with Allah will become difficult. For example everyday recite Dua e tawassul with focus to attain connection with the Imam and ask them to help you find a solution.