62.
教授になってまずはこの大学を変える…
I'll become a professor, and at first I'll change this university
(that sentence had been claimed by Zizka; but I put it here also as it makes a whole thing with the following ones)
全国にある永大の関連病院を変える…
I'll change the hospitals in connection with Eiroku University all around the country...
全国 (ぜんこく) : whole country
関連 (かんれん) : connection, relation; so I suppose 永大の関連病院 are the hospitals in relation with Eiroku University; and 全国にある (existing all around the country) is an attribute of such hospitals
そして日本の医療を変える!
Then I'll change the medical care of Japan!
医療 (いりょう) : medical care
変える (かえる) : to change (1-dan, transitive)
… kind of a bit megalomaniac goals, ね?