I've checked the config for each interface and all 3 show the same:
ping enabled, telnet disabled, SSH enabled, SNMP enabled
web enabled, ident-reset disabled, SSL enabled
It's worth noting that I can only access the webgui and SSH from the Untrusted zone. The Trusted zone, along with the other zone, is completely inaccessible. It doesn't even respond to pings!
I set up traffic sniffing, it works fine for the interface that responds to everything. But when I tried it on the problematic one, it was like it wasn't even connected. My initial suspicion was defective hardware, and I'm beginning to think this is so.
I do realize that having such things open is a security risk, but I need to troubleshoot the problem to get it working first.