What problems did the Communists face upon coming to power in 1949?
After winning the Chinese Civil War, the communists faced two main types of problems. These were economic problems and political problems.
Politically, China was in something of a mess. It had not truly been united in decades. There was not an existing governmental structure that the communists could come in and use for their own purposes. Therefore, the communists essentially had to build a system of government from scratch. This is not an easy thing to do.
Economically, China was, if anything, worse off than it was politically. The country had never been rich. Then, for much of the past few decades, large parts of it had been occupied by Japan. World War II and the civil war resulted in much destruction. The Soviets had taken tremendous amounts of physical plant out of Manchuria after they defeated the Japanese occupiers there. This meant that the Chinese economy had reverted in many ways to one that was based on subsistence farming.
In short, the Chinese Communist Party had a huge task ahead of it when it came to power. It had to rehabilitate the country both economically and politically.