Just to check, do you not have any kind of agreements with any other airlines? Most airlines have *something* with others, it seems. GRU does mean that airport, yes. If you go to Madrid or Barcelona, you can go from Sao Paulo, Rio de Janeiro, or Brasilia to Atlanta (if it is not too full, winter could be bad) and then to Madrid or Barcelona from there. If you fly from Sao Paulo, you could go to New York instead of Atlanta.

In other words, if you can only fly Delta, your options are these:
BSB-ATL-BCN
BSB-ATL-MAD
GIG-ATL-BCN
GIG-ATL-MAD
GRU-ATL-BCN
GRU-ATL-MAD
GRU-JFK-BCN
GRU-JFK-MAD

(BSB = Brasilia, GIG = Rio de Janeiro, GRU = Sao Paulo, ATL = Atlanta, JFK = New York, MAD = Madrid, BCN = Barcelona)