What, pray tell, is the difference between a real word and a new word invented?

Reminds me of an author who was given a brand-new Oxford English Dictionary (a 20-volume English dictionary with etymologies) by one of his fans. His wife was proof-reading a new manuscript when she came across a word that she was sure wasn't real English. He said "Oh, I'm sure it's in the dictionary!" so she went to look. A few minutes later she comes in, throws the volume at him, and storms out. Confused, he flips to the word in the volume and finds the etymology is... his earlier book!

This is a real problem, especially in Homeric Greek and Biblical Hebrew. One approach to figuring out what such words mean, is to go to similar words in related languages. Another is to use earlier translations (such as the Septuagint from Hebrew to Greek in the first or second centuries BCE), when the translators likely had a better sense of what the words meant.

I believe most hapax legomena to be cromulent.

Are you just trying to embiggen the cromulence around here?