OpenGL / depth test glitch?

Hello,

I am rendering a load of points via an OpenCL VBO but the image is coming out oddly. Code is as follows:

ofEnableDepthTest();
ofEnableBlendMode(OF_BLENDMODE_ALPHA);

glEnableClientState(GL_VERTEX_ARRAY);
glEnableClientState(GL_COLOR_ARRAY);

glBindBufferARB(GL_ARRAY_BUFFER_ARB, vbo);
glVertexPointer(3, GL_FLOAT, sizeof( float4 ), 0);

glBindBufferARB(GL_ARRAY_BUFFER_ARB, cbo);
glColorPointer(4, GL_FLOAT, 0, 0);

glPointSize(1);
glDrawArrays(GL_POINTS, 0, counter);

glBindBufferARB(GL_ARRAY_BUFFER_ARB, 0);
glDisableClientState(GL_COLOR_ARRAY);
glPopMatrix();
ofEnableAlphaBlending();

Where the alpha blending of the points is set at 0.1. The images below are meant to show one cloudy disk, but half of the points appear to be occluded in some way and there is a plane appearing also.

How can I fix the occlusion issues in the output image?

The above seems to be caused by calling the ofEnableDepthTest();

I guess it is an interference issue with the points render

Does anyone know a work-around or fix for this?