Hello, it shouldn't have any trouble connecting to that Modem via Ethernet!?
The Interface that connects to the Internet, needs to be drug to the top of System Preferences>Network>Show:>Network Port Configurations and checked ON.
Does the Ethernet show any IP at all in System Preferences>Network>TCP/IP tab?
Is Configure IPv4 set to Using DHCP?
Yeah, the 169.254.x.y IP is when it can't get an IP via DHCP, might try Manually if you know the Routers IP.
The internal, LAN-IP address is normally set to a default, private number. Linksys routers, for example, use 192.168.1.1 for their internal IP address. D-Link and Netgear routers typically use 192.168.0.1. Some US Robotics routers use 192.168.123.254, and some SMC routers use 192.168.2.1. No matter the brand of router, its default internal IP address should be provided in documentation. Administrators often have the option to change this IP address during router setup. In any case, however, the private LAN-IP address remains fixed once set. It can be viewed from the router's administrative console.
So if the Router was 192.168.2.1
Subnet Mask :255.255.255.0