very good;
eth0 Link encap:Ethernet HWaddr 00:13:8F:B3:32:C3
inet addr:192.168.62.52 Bcast:192.168.62.255 Mask:255.255.255.0
UP BROADCAST MULTICAST MTU:1500 Metric:1
the UP says your NIC is running
(fyi: you can control this with ifconfig eth0 {up,down}
the addr: and Mask: are just fine
so, we have hope that this is workable.
now try to access the router via your browser. from your addr: info,
it looks like it would be 192.168.62.1, but that's not any known default ...
did you change it? get your setup info for the router -- it will tell you
the DEFAULT router lan address -- the usual addresses are
192.168.0.1; 192.168.1.1; 192.168.2.1
keep trying one of these and take not which one works (if any).
without any hard docs on your setup, I will guess that nothing will work
and we will need to reconfig the NIC.
fyi: the system nic must be in the same subnet as the router,
eg: router 192.168.0.1 and the system nic might be anything like 192.168.0.X