Step 1: Decode the eponym. The Sabin-Feldman dye test is named for its developers and is the gold-standard serology for the protozoan $Toxoplasma\ gondii$.
Step 2: Mechanism - viable tachyzoites are mixed with patient serum and complement. Specific antibodies lyse the parasite so its damaged membrane will not absorb methylene blue; unstained organisms therefore mean a positive test.
Step 3: A positive result confirms exposure to Toxoplasma, so the condition diagnosed is toxoplasmosis.
Step 4: Discard the rest - botulism needs toxin assay, sarcoidosis is a biopsy/ACE diagnosis, and yellow fever is a flavivirus picked up by serology or PCR. None relies on dye uptake by a living parasite.
\[\boxed{\text{Toxoplasmosis}}\]