Say that you want to have a Primary Key on columns (a, b, c, d). You can identify duplicate rows this way:
WITH CTE AS (
SELECT *, COUNT(*) OVER(PARTITION BY a, b, c, d) AS valuecnt
FROM tbl
)
SELECT * FROM CTE WHERE valuecnt > 1
It will be quite a mess to sort this out. It would probably have been better to keep the keys and had the two databases in parallel and try to run updates. But that would also be a lot of work depending on how much data the users have entered.
And by all means stay way from that Design screen! The Table Designer in SSMS is horribly buggy and can lead you into even deeper troubles.