You mention an old Dell laptop but not the operating system. Have you updated drivers recently particularly the ethernet controller/network adapters?
Am I right in then assuming that you decided to make a wireless connection - again are the drivers for this up to date - this is where you can get updates from .
Click on start, control panel, network and sharing centre, manage wireless networks, change adapter settings (right side ) right click on the Wireless Network Connection and click on properties, Under the network tab, click on Internet Protocol Version 4( TCP/IPv4 ) and click on properties, and check the box that says Obtain an IPv4 address automatically, and Obtain DNS server address automatically, and click ok.
It could be that you are running IEEE 802.1x authentication, but are not actually in a 802.1x (EAP) environment.
If this is the case try this:-
Start --> Programs --> Accessories --> Communications --> Network Connections --> Right-click your Connection and select Properties --> Click on the Authentication tab --> Disable / uncheck the option IEEE 802.1x authentication for this network. Now, try to connect to your Wireless network; are you able to? (Note: you may need to restart the computer.)
If for some reason the option to uncheck the 802.1 is greyed out then check your settings are on WEP not WEA in your network set up. You will need the WEP code to set this up which is usually on the base of the router.