your IP address is obtained from aol, the problem will be with wireless encryption. you need the WEP key from the router. if its a netgear router open your browser and type in the address bar 192.168.0.1, this will take you to the router config page. (if you are asked for a username try username or netgear, the password should be password) look for wireless settings, there should be a security option there with a WEP key (26 characters). copy this code down exactly. Also take a note of the router name, this should have SSID in brackets, if its a netgear router should just be netgear. This is needed to give the network the correct name. then set up a wireless network.
If you have a speedtouch router, open your browser and type www.speedtouch.lan and again look for wireless settings, security.
when setting up the wireless network enter the SSID name then choose to assign a WEP key, type in 26 character code taken from router. unplugg the cable. once you have completed the setup you should now be connected with a secure connection (i.e. no one else can access your network without the WEP key).
RESPONSE FOR MB
The IP address IS obtained from the ISP in this case AOL as AOL support DHCP (Dynamic host Configuration Protocol) if you go into network settings and check the proerties of internet protocol you will see that the laptop/computer will be set to obtain ip address automatically, unless they are assigning a static ip address which is done by the owner/user of the PC/laptop.
I accept what you are saying MB (by the way, not arguing, just discussing) while we are both correct the situation seems to be that the router wont allow wireless connection. Mouse can get access with a wired connection showing that IP assignment is working on the router, still possibly a security issue.
RESPONSE FOR MOUSE:
you said that the router is not a netgear, if you got the router from AOL its most likley to be a Thompson Speed Touch 576 or model very similar. The settings for IP addresses along with DHCP and NAT should all be automatic which you probably wont have access to anyway. The fact you are getting connection with a wired connection suggests its still a problem with wireless security, I know its a pain in the *** but you should double check the WEP key. Also check the encyption strength, make sure its at its highest.