What's wrong with your HDRI rendering?  It looks good to me.  But seriously
folks... It appears that maybe you have rotated the HDRI sphere so that the
bright spots are underneath your plain (and plane).  That means the only
thing illuminating your scene is the rather dull floor.  Make sure the up on
the HDRI is aligned with the normal of your plane.

You're not going to get well defined shadows with HDRI so I like to back the
shadows up with a dim point light or area light (if you've got the computer
for it).  Try adding one aligned with the bright spots on the HDRI so that
illumination lines up and make it real dim so the scene doesn't wash out.

Radiosity is all about tweaking and more tweaking.  Try these radiosity
values for some higher quality but a slower redner, and play with the
assumed gamma in your global settings to give the image some contrast.

global_settings {
  assumed_gamma 2.0
  radiosity {
    pretrace_start 0.08
    pretrace_end  0.01
    count 1600
    nearest_count 10
    error_bound 0.5
    recursion_limit 1
    low_error_factor .25
    gray_threshold 0.0
    minimum_reuse 0.015
    brightness 1
    adc_bailout 0.01/2
  }
}

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