Way I graded the papers
What I did is use a statistical method called Cronbach's Alpha, and I cut out the questions that I could see that you had problems with. This left 18 questions for both sections.
The overall average was still low, so what I did was shift the distribution of the grades from a mean of 54.5 to 82 and reduced the standard deviation from 13.7 to 5.
It means the lowest grade of 17% was changed to a 62 and the highest grade of 94% went to 97%. I've included a photo of the distribution using this curve.