
But I bought a copy of the Logos Iliad, and am going to give it another try. I decided to try a "text-directed" approach, where I take lines of Homer, look up the lexical forms of words (thanks, Logos!) and try to decline them.
I'm stuck on line 1, word 2.

OK, in my cheap version of Liddell/Scott, I find (with diacritical marks that don't show up here):
"ΑΕΙΔΩ - Att. contr. αδω; impf. ηειδον, Ep. αειδον, Att. ηδον: fut. αεισομαι, Att. ασομαι, Dor. ασευμαι; rarely αεισω, Att. ασω, Dor. ασω: aor. I ηεισα, Ep. αεισα, Att. ησα: -Pass., aor. I ησθεν: pf. ησμαι: -to sing ..."
Stripping out the parts I think I don't care about, I get...
"ΑΕΙΔΩ - impf. Ep. αειδον: fut. αεισομαι: aor. I Ep. αεισα: -Pass., aor. I ησθεν: pf. ησμαι: -to sing ..."
Going to my copy of Goodwin and Gulick, I find:
"463. The principal parts of a Greek verb are the first person singular indicative of the present, future, first aorist, first (or second) perfect active; the perfect middle, and first (or second) aorist passive; with the second aorist (active or middle) when it occurs. If there is no future active, the future middle is generally given (450)."
My copy of Pharr has something very similar.
What I get from this is that the principal parts are (in Epic):
present indicative active
αειδω
future indicative active
αεισομαι
first aorist indicative active
αεισα
first perfect indicative active
?
perfect indicative middle
?
first aorist indicative passive
ησθεν
Is ησμαι 1st perfect indicative active? Perfect indicative middle? And is a mere human expected to be able to figure out how to determine the principal parts of vowels based on a lexicon entry, much less conjugate them?