If you can give more description as to what you have at home, what type of router, setup, what type of network security...etc.
I connect fine to both my network and my girlfriend's. Only had to type the password once, and now the OS remembers it and connects to either one of my preferred networks when they're available.
Click on System Preferences, Network, Airport and from the drop-down list, you can either leave it to Automatic or Preferred Network. Make sure your network is in the preferred network list, you should be ok.
Good luck.
Edit: If the network is secure, make sure you're using the same security type on the laptop as the one you have on the router. (WEP, WAP, WAP2, etc).
I had a customer who couldn't connect to his home network (similar problem to yours) and I told him that. He tried using a different security setting (WEP, WAP...etc) and that fixed his problem. Try that, let us know if it worked.