I think you have something weirder going on here. I would have thought you wouldn’t get as far as seeing a window if jars were missing, or at least see an obvious error message.
Maybe try porting the specs test example (from Examples / Demos / Tests) and compare the output in Processing and Eclipse.
size(100, 100, P3D);
PGraphicsOpenGL pg = (PGraphicsOpenGL)g;
println(PGraphicsOpenGL.OPENGL_VENDOR);
println(PGraphicsOpenGL.OPENGL_RENDERER);
println(PGraphicsOpenGL.OPENGL_VERSION);
println(PGraphicsOpenGL.GLSL_VERSION);
println(PGraphicsOpenGL.OPENGL_EXTENSIONS);
Well, the second is very, very deprecated!