I can a wireless laptop still work without wireless connection being installed as I don't have any wireless connection anywhere around the house just a normal phone socket where my desktop pc is and I am on dial up.
You won't be able to connect to the internet on your wireless connection, unless you can detect a neighbours wireless access point, as roomby has said. However, you can of course connect via your dial up modem as normal.
You can purchase a wireless router very cheaply (I think I paid �50 for my linksys one) but they will only work on Broadband (I think).
You can try and discover other local services and see if there are any around, for example in my flat I can connect to 3 other networks. They should be secure (like mine is) but the people haven't done this so I can connect to the internet via somebody elses network.