When trying to use his Sonic CS Ethernet card, Richard Murray would get a message that said "Couldn't switch to Ethernet due to an error." He found that dragging the Ethernet CS card driver from the Sonic Systems installation floppy to the System Folder solved the problem. In other cases (possibly with other Ethernet cards), simply making sure that 7.6's Ethernet CS card driver is installed may do the trick.
Greg Morin noted that, on his Performa 636CD with an Apple Comm Slot Ethernet card, the 7.6 Installer mistakenly installed the "Ethernet LC" extension and not the "Ethernet CS" extension. He had to do a Universal install to get the "Ethernet CS" extension installed. Until he did that, he would get an error message that said: "An error occurred, built-in LocalTalk port will be used."
Dan Jahn writes that Dayna Support confirms that the Performa 6400 does not recognize Dayna's Ethernet card if any of Apple's Ethernet extensions are present. If all of them are removed and then Dayna's software is installed, you can get Ethernet on a 6400.