I have a Dell R310 server containing an Intel ET Quad Port Ethernet Adapter, but it isn't detected by ROS 4.16 (FATAL ERROR: no network card found. Interfaces list is empty).

If I install ROS 5.0rc7 the interfaces are all detected OK. When I check system > drivers, the Intel card uses the e1000 driver, which is available in ROS 4 so I'm guessing that it's not a driver issue.

What else could cause the adapter not to be detected in ROS 4, but fine in ROS 5? Might it be because the Intel adapter is PCI-e and not PCI or PCI-X?

almost everything intel makes is e1000 their unified driver only supports cards up to that release. you need a new e1000 driver for newer cards, this is why 5.x works and 4.x doesnt.