Since I haven't the table structure, and no data to test, I'm not absolutely sure about the result. But this should have to work if you have at least SQL Server 2005 as RDBMS.
WITH CTE_DCIPS
AS (
SELECT ROW_NUMBER() OVER(PARTITION BY J_CaseNum, J_Index ORDER BY Ind_Last_NM) RowNum
, J_CaseNum
, J_Index
, J_VehicleIndex
, J_PersonIndex
, J_CaseNo
, J_PersonID
, Ind_Last_NM
FROM dbo_DCIPS
)
UPDATE tbl
SET tbl.J_PersonIndex = RIGHT('00' + CONVERT(varchar(5), cte.RowNum), 2)
, tbl.J_CaseNo = tbl.J_CaseNum + tbl.J_Index
, tbl.J_PersonID = tbl.J_CaseNo + tbl.J_VehicleIndex + RIGHT('00' + CONVERT(varchar(5), cte.RowNum), 2)
FROM dbo_DCIPS tbl
INNER JOIN CTE_DCIPS cte
ON tbl.J_CaseNum = cte.J_CaseNum AND tbl.J_Index = cte.J_Index