Thomas: I am fairly convinced that your plants are suffering from a lack of nitrogen in the soil. Two things are happening. First, all the compost organisms have grabbed the "free" N and are using it to build their population and ultimately make good compost out of the less composted portion of the mix. So you have to feed both the composers and your crops!   Few organic fertilizers have N that releases quickly, which is what your plants need now. If you want to only use organic products, email me and we can talk about  options. A conventional product like Miracle-Grow or others would give fairly quick results if you use according to directions. In the future, make sure you some N in the soil mix before you start planting. Feel free to email me if you have more questions: <personal data hidden> (recently retired). 

Would lime in the fall help the compost break down? I would like to help the garden area get healthy. I also have 16-16-16 fertilizer.  The only organic option I've used in the past is the compost.

Lime would have an impact on soil pH which is related to nutrient availability and uptake. But it isn't the cure here. It takes a very long time and the rain each winter washes all the:"free" N away. 
 
The nitrogen in triple 16 is generally urea (possibly made by Dyno in Columbia City). Alone, it is soluble and is fairly quickly available. So is calcium nitrate and ammonium sulfate (21-0-0). 

It still might be better to use some quickly soluble and available product like the Miracle-Grow or something similar along with some side-dressing  with the triple 16. It will take a about 2 weeks to see a response in corn (a deeper green color in the leaves), a little bit slower  with the other crops.  Hope this helps. Chip