Why doesn't Diabetes cause death by starvation?
Not all cells depend on insulin to take in glucose from blood (e.g. vascular endothelial cells). But the majority do (muscle tissue and fat tissue).

The lack of insulin causes the cell to use auxiliary metabolic pathways to generate its energy [1]:


in muscle, the protein breakdown is stimulated
liver gluconeogenesis is stimulated by low insulin levels and high amino acid levels in blood and using substrate from muscle and fat tissue
glucocorticoids stimulate lipolysis
liver starts ketone body synthesis, which along with medium chain fatty acids prove to be quite a good alternative energy source for the brain


Energy from nutritional principles is as follows:


Lipids = 9 kcal/g
Proteins = 4 kcal/g
Carbohydrates = 4 kcal/g - the most important because they are used as is. Lipids and proteins require energy from other sources to start chemical reactions which yield energy.


References:


Mark Brandt, Ph.D. Endocrine Notes Supplement from Rose Hulman Institute of Technology, pages 78-80  
Wikipedia (links)