>>> However, when my wife logs on under her user
>>> account on the same PC see cannot get an
>>> internet connection whereas I do.
Are you connecting to the router by ethernet cable or "wirelessly"?
If "wirelessly", while logged in with your wife's account have you "Connected" again to the wireless network?
>>> I have read that it is advisble that you should disable the SSID
There are other security measures you can take without having to disable broadcasting of the SSID. Enable encryption of the wireless network using WEP or, preferably, WPA and use MAC address filtering so that only those adapters whose MAC address has been entered into the router's settings can connect to it.