LOL! I have an LC case with an LC II Logic Board in it, and a LC II with a LC Logic board in it. I managed to get these systems separately and months apart, so they were not from the same seller. It just happened to happen that way. I could switch the boards around to get them into their appropriate cases but for now I have not.
But as stated, the LC Logic board need that plastic piece with the fan and speaker on it, and it is there inside the LC II Case.
IDK about the LCI/II/III as I never got the card I have working on my LCII beyond maybe installing the drivers and a green light of some sort.
But I will note that I had similar trouble with my Power Mac 6100/66 not playing nice with a more modern 10/100 Mbps (Fast Ethernet) switch or hub, whereas interposing a 10 Mbps hub in between it and more modern hardware solved that problem (probably a similar auto-negotiation/duplex problem).