upgrading network card/router

When I ordered my Dell Inspiron 9100, I accidentally selected the 440x 10/100 Integrated Controller (11mbps) without knowing a 100mbps option was available. Then I purchased the Netgear Router ( Model: MR814v2) and started to suffer extremely slow browsing and downloading speeds.

 

So my question is, should I upgrade to Dell's 100mbps network card and purchase a new router that's compatiable with 100mbps? If so, can I just send in the laptop and get the card replaced by Dell?