The first thing which is important to note is the difference between taste and flavor.
Taste refers to the chemical sense performed by taste buds present on the tongue, and to date there have been identified 5 tastes: sweet, bitter, sour, salty and umami. Thus I understand obstructed nose and sinuses should have no significant effect on taste.
Flavor, on the other hand, is the final sensation that conveys the information about the food we're eating, and involves not only taste, but also smell, mechanical sensation (like that smooth flavor from cream) and pain and temperature pathways (hot and spicy food, like peppers). Part of the signals from all these receptors located on the mouth (and nasal) cavity ultimately converge to the same location in the brain, where they are processed to create the final flavor (I know taste and smell do converge to the same region, cannot tell the others with full certainty).
So, having obstructed sinuses and nasal cavity can interfere with the smell detection (by not allowing molecules to bind to receptors on the olfactory epithelium), and thus interfere with flavor.
You can check this site which I think explains very well what I am trying to pass on, it is very clear and covers all the physiology that I talked about, allowing you to go deeper into details if you are interested: http://www.cardiff.ac.uk/biosi/staffinfo/jacob/teaching/sensory/taste.html and also http://www.cardiff.ac.uk/biosi/staffinfo/jacob/teaching/sensory/olfact1.html (you have to scroll down to the main text)