... locates the word 'hello' then if the rest of the string ...

This is your first problem: a lookahead peeks into the string, but doesn't change the position that the rest of the string will attempt to match at. You don't want a lookahead for this, but a straight match - then the rest of the pattern will correctly be tried against the rest of the string:

  /^hello.../
[download]

... if the rest of the string DOES NOT contain the char 'G' followed by the char 'a' ...

A simple negative lookahead:

  /
    (?!   # fail to match if you find (
      .*  #   zero or more characters
      Ga  #   followed by "Ga"
    )     # )
  /x
[download]

So your specification is satisfied simply by:

  /^hello(?!.*Ga)/
[download]

Hope this helps,

Hugo