AFAIK Genesis is based on AmiTCP and during the install process (of Genesis, under 3.9) several folders and assigns for AmiTCP are created. I don't think this is the same thing as actually "running" AmiTCP, it's just tacking on to some of the various folders that are part of the overall AmiTCP package.
Your actual program that you run to start the Internet connection is Genesis.
Since your error message is telling you that it's "unable to open genesis.library", have you checked in LIBS: what version you have installed there?
Sorry to hear you had problems with Roadshow, too. Guess I'm not the only one who's cursed, lol.

You might also check that the following lines exist somewhere in your S:User-Startup:
Assign AmiTCP: SYS:Internet/Genesis
Assign C: AmiTCP:Bin ADD
Assign AmiSSL: SYS:Internet/AmiSSL
Assign LIBS: AmiSSL:Libs Add
Path AmiSSL: Add
(I've got tons of assigns in my user-startup, but those looked like they might be relevant, lol)
Actually, re-check that genesis.library version # again. I don't run Genesis (haven't used it since a brief period in the 1990's), but I see I've got 45.4 in SYS:Internet/Genesis/libsYour assign or your path might be screwed up, and it's not able to find this file.