Break the case down. Acute renal failure, anuria, and a normal ultrasound together tell us the collecting systems are not dilated, so post-renal obstruction is unlikely. The remaining question the clinician wants answered is how well the kidneys are actually working, which is a functional question.
A technetium-99m DTPA renal scan answers exactly that. DTPA is cleared purely by glomerular filtration, so its renogram tracks GFR, relative function of each kidney, and renal perfusion. It does this even when excretory function is poor, because the gamma camera detects the tracer regardless of how little urine is made.
The contrast studies fail this test. An IVP depends on the failing kidneys excreting nephrotoxic iodinated contrast, so it gives faint images and risks worsening the injury. Retrograde and antegrade pyelograms are invasive maps of the urinary tract aimed at finding blockage, not measuring function, and obstruction has already been excluded.
So the functional radionuclide study wins.
\[\boxed{\text{DTPA scan}}\]