I am in an interesting situation, and I was wondering if someone could help. 

I am planning to return to Germany to reconnect with my ancestry and extended family, and also because having already lived in Europe for a bit, I just don't like America, especially Texas. I could probably get a legit work visa after doing maybe a few more years of grad study there, which I plan to do anyway in Economics, but I think this route would be easier for tuition purposes.  My paternal grandmother was a German citizen who married an American GI who was himself German a few generations back but not close enough to matter. My father was born in an American military hospital in Frankfurt, Germany. I do not know if my grandmother ever renounced her German citizenship, but if she did, according to relatives, she did so after my father was born. My father is definitely NOT a dual citizen. And, of course, everyone concerned was born before 2000 when a new law took effect that modified the German blood citizenship route for those born after that date to make it no longer possible in most cases. That new law does not apply to me since I was born in 1986. 

Now, the law is still a bit confusing to me. If my father was born to a German parent, does that mean I can claim German ancestry through him via my grandmother? Or would he himself have to have claimed German citizenship at some point? I know, were my family Irish, my connection would be strong enough, but the German law is more ambiguous on this point, and I'm wondering if it would be possible if I could get my father's and grandmother's birth certificates and naturalization certificates to prove that my father was born a German citizen, or if I could otherwise claim German citizenship for myself?