As far as the Hebrew הִתְפַּלֵּל (hitpallēl) goes, I’m pretty sure1 the only example of prayer clearly directed at people (rather than God/gods) is Isaiah 45:14, which doesn’t come across as "pray" in most translations I’ve looked at, presumably because the idea is troubling.
Thus says the LORD:
“The wealth of Egypt and the merchandise of Cush,
and the Sabeans, men of stature,
shall come over to you and be yours;
they shall follow you;
they shall come over in chains and bow down to you (אֵלַיִךְ יִֽשְׁתַּחֲוּוּ)
They will plead with you (אֵלַיִךְ יִתְפַּלָּ֔לוּ), saying:
‘Surely God is in you, and there is no other,
no god besides him.’” (ESV)
The phrase "plead with you" uses the verb/stem of interest (hitpallēl) with the preposition אֶל (ʾel = "to", here in its emphatic form), which standardly identifies the object of prayer. The object ("you") is feminine singular and thus probably refers to Jerusalem rather than Israel (which is consistently referred to using masculine pronouns) or (more problematic still) Cyrus. The semantically related verb יִשְׁתַּחֲוּוּ (yištaḥăwwû = "they will bow down") - makes it all the more jarring.
There is another set of occurrences of this same verb + preposition pair (hitpallēl ʾel) that is usually translated differently but involves precisely the same Hebrew construction. This is exemplified by 1 King 8:29 // 2 Chr 6:20:2
that your eyes may be open night and day toward this house, the place of which you have said, ‘My name shall be there,’ that you may listen to the prayer that your servant offers toward this place (yitpallēl....ʾel–hammāqôm)
Here, as in other similar examples 1, hammāqôm ("this place") refers to the temple. The preposition generally translated "toward" is ʾel, the same word used to denote the recipient of prayer elsewhere.
With regard to the Greek terms, both the noun προσευχὴ and the verb προσεύχομαι are applied exclusively to the religious sphere throughout both the LXX and the NT. This distinguishes the term from εύχομαι, a more common word outside of Jewish literature where it often carries a sense of "to vow".3
1. "Pretty sure" because this is drawn from David Clines’ Dictionary of Classical Hebrew, which comprehensively catalogues the objects of this verb + preposition combination in the entire corpus of known Classical Hebrew.
2. The notation // indicates parallel passages. See also: 1 King 8:30 // 2 Chr 6:21; 1 King 8:35 // 2 Chr 6:26; 1 King 8:42 // 2 Chr 6:32.
3. Heinrich Greeven. "εύχομαι". Theological Dictionary of the New Testament, Ed. Gerhard Kittel, trans. Geoffrey Bromiley. Eerdmans, 1964.