How do you answer the question, "What date did the applicant became disabled or unable to work?" when there is not an exact diagnosis date in medical records?

The date the applicant became disabled is not necessarily the date that he/she was first diagnosed. SSA is looking for the date on which they were unable to work at a substantial gainful level due to their illnessess/conditions.  You should enter the date that they were no longer able to work (or last worked at an SGA level).