I posted in alt.callahans in 1994. Until they had a big fight and I got disgusted and left. IRC’ed since Dec 94.
BBSing… Since about 1986. 
Another c64 + 300 baud modem user here.
My first BBS post was a question on how to solve one of the puzzles on Leisure Suit Larry.
Well, i guess it would depend on what you’d call the “Internet”.
My first post to an online forum was on the NORAD BBS in Orlando, in 1989. I was asking about what was a good communications program, since the one i had was lousy (i eventually ended up using TeleMate). I was 12 at the time.
My first post to a national online forum was on the Music BBS on Prodigy, talking about a They Might Be Giants concert. 1991.
My first Usenet (and therefore most appropriately termed first Internet post) was a question on inline skating on rec.skate. 1994.
And mine was in the same place, shortly after. Man, it’s been almost 10 years, zyzz! 
My first BBS post was in 1985.
First post to Usenet was in '87 or '88; don’t remember which, but it was before the alt.* groups were created…
I posted to alt.college.fraternities.sororities back in '93, but, yeah, I had probably posted something, somewhere, back in the 80’s with a mighty Apple II+, I believe [sub]though I could be wrong[/sub].
I was right there with Danalan in the 80s with my trusty C-64 on the original Compuserve, but that’s not really the Internet.
I think my first post to USENET was in 1992 or so on one of the guitar-related newsgroups. I can’t remember which one.