Why is 我很要... an invalid statment
I'm a native Chinese speaker. 

If you want a cup of coffee, it is okay to say:


  我要一杯咖啡


but actually, in most cases, you should say:


  我想要一杯咖啡


This is because "想要" is more polite, although "want" means both "想要" and "要" if we directly translate it.

Regarding your question, if you want to tell people that you really want something (or to do something), you should say it in a polite way. So you should say


  我很想要一杯咖啡


By the way, if you feel this complicated, you can simply forget the expression of "我要 + something", and just say "我想要 + something" everywhere.