A couple of thoughts:
Assuming this is dial-up (since you say "going online")
Are you using the same telephone accesspoint and modem cable for both machines? If not, then try the cable and access point from the machine that works on the machine that doesn't. If that works, fine, you can then pin it down to your cable or access point by substituting them one at a time.
If it doesn't then the problem is either inboard of your computer or something at the Freeserve end.
First your computer.
Is your modem working? Check in device manager. Is it installed and ok? Somewhere on the modem properties there may be a device check. Use this to see if it is sending and recieving.
Compare your connection properties with your wife's? Are they identical?
Then the freeserve end. Are you using a different id? If so try usin your wife's id on your machine. If this works then it's a problem with your id. Check if it is enabled by calling their helpline. Many ISP's disable id's when they haven't been used. At the same time check if you have the correct id and password.
If none of this works, post back.