there should be no problem, because 10/100M is downward compatible with 10M(and also SCV is only 1.5M maximum theoretically).
Why do not you read the Router menu see whether there is anything you can configure.(for most of the router, even you can not connect to outside, you computer will be able to find the router, between computer you will be able to communicate, and access the router configuration menu, for instance, SMC router normally use 192.168.123.254 as the configuration interface, downthere you will be able to find related information, e.g., the DNS that SCV passed you and so on.)
hope can help you. why not tell us your router Model number so that the problem can be more specific?