It wasn't as much of a problem that made Descartes go back to square-one as it was the need to lay the groundwork for a more concrete set of assertions. He was bothered by the mysticism that had found its way into Philosophy. Having a background in both Physics and Mathematics, he tried to bring geometric precision to what he dealt with. Just as importantly, he realised very early on that reason and faith must be separated, and most would agree that he did a good job at it.
Now, since Descartes' philosophy rests to a good deal on the concept of self-evident facts that can be proven without assumptions, I feel it's important to point out that these 'self-evident facts' could only be proven through one of two process: induction or deduction. Without them, any articulated thought would by default have limitless scope. So, and it's purely my opinion, Descartes' philosophy was inherently corrupt.
I'd like to quote a little something from Descartes that sheds light on how he wanted to go about the undertaking:
The first (rule of method is to) never accept anything true which I did not clearly know to be such; that is, carefully to avoid haste and prejudice, and to include nothing more in my judgements than what was presented to my mind so clearly and distinctly as to exclude all reason for doubt.
And more than the turn towards sciences and rationalism in the time period quoted, there was the question of how to add clarity to all disciplines and remove any chance of doubt.
This is the question that the philosophers of the 16th and 17th century occupied themselves with. And you can see two very distinct approaches to this. One was from Descartes, and the other from the British empiricist John Locke.
Descartes voted reason whereas Locke felt that the answer lay in the nature of knowledge.
And so this was the main aim of Descartes, to answer the one question that had been asked for ages:
What, if anything, can ever be known for certain?
He also sought to integrate certain concepts of Physics, Theology, Philosophy and Mathematics that would in turn, he felt, help us scrutinise the contents of each subject better.
For Further Reading:-
1) An Essay Concerning Human Knowledge BY John Locke
2) Discourse On The Method of Rightly Conducting The Reason BY Descartes
3) Kierkegaard and Descartes BY Ronald Grimsley