Picking without depth-buffer information[SOLVED]

What are the less difficult ways to implement picking without relying on the depth buffer information ?

I was successfully using gluUnproject untill I faced an unresolved issue with depth buffer being cleared after I blend an FBO.

That’s why I unfortunately have to disregard solutions based on the depth buffer.

Thanks in advance.

For the information,
my 3D scene consists in a sphere (virtual globe) with lines on it representing the political boundaries between countries of the world.

So I just need to pick the point on the sphere that coincides with the mouse position.
Once I get the x,y,z of that point, I can easily deduce the longitude/latitude which are my final goal.

Take a look here:

Thank. I just solved my issue by calculating the intersection between my scene sphere and the line joining the far/near points coinciding with cur mouse pos.