believe in, a. to be persuaded of the truth or existence of: to believe in Zoroastrianism; to believe in ghosts.
b. to have faith in the reliability, honesty, benevolence, etc., of: I can help only if you believe in me.
http://dictionary.reference.com/browse/believe+inStrikes me as reasonable. I can believe in God or believe in Obama, I can believe in evolution or in the resurrection from the dead. It accounts for all the data, even the data nobody mentioned. (Most people really suck at producing syntactic paradigms. Given an example, they can replicate it, but spreading out to completely different lexical fields, trying different kinds of lexical categories or complements is beyond them.)
That people have a feeling that mythical things are properly the object of the preposition is captured by "persuaded by": most of us don't need to be persuaded of things that are observable.
When it deals with mythical or unprovable things, the distinction between the first two can be blurred. To believe in God's reliability or honesty requires first believing that God exists.
Can the idea that the "in" comes from the OE infinitival ending. There's no need to posit an aberrant phonological history for that one verb when it's readily attested without the "in" in many contexts, and is more common without it. In other words, it's simply much less likely and a historical linguist would select that as probably his last option. Actually, he's more likely to just reject the idea and say "unexplained".
That "in" has parallels in Russian (verit' 'believe' verit' v 'believe in') and, oddly, Biblical Hebrew. I'm sure Langacker would have fun with it. The Russian is probably calqued from French, IIRC, and I'm not above speculating that English may have recast 'believe/believe in' as parallel to French croire/croire en. Koine doesn't have anything like "in" after pisteuo 'believe', many Bible translations notwithstanding, but I usually think of it as meaning "have faith" more than "believe"; that may just be translating the English back into it, but that nifty -eu- stem marker really sounds to my ears like the Slavic -ov-, a nice way to make denominal verbs. Pistos 'faith' is a noun in Gk (and "believe" for me really isn't denominal).
On the other hand, French got their "en" from somewhere. Perhaps they just wanted to formalize the dative that Latin credere required. Perhaps there was a semantic nuance that consistently followed "in" or "en". I don't like that, though, not on principle but because I tend to dislike big fuzzies in historical syntax. It strikes me there are two believes: one is intransitive and the other is transitive. The transitive one always asserts that there are two possible truth values of an utterance, fact, or narrative, and selects the value "true" (rejecting "false"). The object has a funny sort of theta role. But things don't have truth values. So when we apply the verb to a person, we say not that the person has the truth value "true", but that his utterance or narrative is true. That leaves uses with things and persons in which it's not the utterance that's at issue, but the older meaning of having trust in or belief in some global sense. Since the verb at some level of semantics is intransitive, English has a nice out--it finds some preposition to make a complement possible in some other sense. (Or as Chomsky and Fillmore would have put it at some point, to assign case and thereby license the noun's presence in the sentence. If you like Chomsky.) Note the early variation, where believe in/on/of all had the same meaning.
I guess the passive ("Picts are believed to have been non-Indo-Europeans") seems to say that's wrong, but English allows the subjects of embedded clauses to raise to subject position if the subject is a dummy: "It is believed for Picts to have been non-Indo-Europeans" or "It is believed that Picts were. . . ". Note the fairly meaningless "for" that in Chomskian terms licenses "Picts" but, in any event, introduces a tenseless clause.)
If you like history, check out the two examples Wiktionary has for gelyfan (
http://en.wiktionary.org/wiki/gelyfan):
Gif ðu soþne God lufast and gelyfest. If you love and believe in the true God.Ðær gelyfan sceal dryhtnes dome se þe hine deað nimeð. There whoever death takes must trust in the judgment of the Lord. (Beowulf, ll. 440-1)
Note: soþne God is clearly accusative even to my untrained eye, not dative, but they hedged on the "love and believe in". But they cutely translated gelyfan dome as "trust in"--I think "dome" is dative. So perhaps we already see the distinction made in English between a dative and an accusative, but with a bit of shifting in the semantics.