Though bare-stem compounding is the usual method in Indo-European, compounds with an inflected first member are actually not uncommon in many IE languages. It seems that all cases could be used. For Greek, Smyth (who calls these "flectional compounds") offers the following examples (879):
A compound whose first part is a case form, not a stem, is called a flectional compound (cp. sportsman, kinsfolk): (1) nominative: τρεισ-καί-δεκα thirteen; (2) genitive: Διόσ-κουροι Dioscuri (sons of Zeus), Ἑλλήσ-ποντος Helle's sea, Πελοπόν-νησος (for Πελοποσ-νησος, 105 a) Pelops' island; (3) dative: δορί-ληπτος won by the spear; (4) locative: ὁδοι-πόρος wayfarer, Πυλοι-γενής born in Pylus.
Some examples from Latin and Sanskrit are given in Kathryn Klingebiel (1989), Noun+Verb Compounding in Western Romance, ch. 2:
- Latin: lēgis-lātor, with genitive first member; manū-missiō, with ablative first member
- Sanskrit: vājam-bharāh "prize-bearing", with accusative first member; amhasas-pati "name of an intercalary month", with genitive first member
ETA: Speaking of Nausicaa, there are a number of other Greek compounds with the first element nausi- clearly functioning as a dative, e.g. ναυσίπορος "traversed by ships, navigable", ναυσιφόρητος "carried by ships", as well as another Phaeacean royal name Ναυσίθοος "swift in/by/with ships".