I did a search of your particular router and it seems relatively basic, read lower end of the spectrum. You said you have a modest size ranch house, how big are we talking about? How many walls is the signal going through? You said your internet is wireless what exactly do you mean? Is your internet completely wireless like clear (formerly clearwire)?
If you are using an ISP like Clear then your router may not be compatible with their equipment. If you are using a wireless router and pulling signals from your neighbor the signals might be too weak for the Wii to connect. If you are using a service like Verizon then you probably have too many obstructions in the way.
Some solutions that I can think of. One, get yourself a more powerful router. Look for a dual antenna, extended range model. These can be had for around $300. Netgear and D-link both make excellent models. Two, move your current setup to a more central location. It sounds like you might have to many obstructions in the way. Radio signals are line of sight and they don't like going through walls very much. If you can't move your computer then consider moving the Wii, the fewer obstacles the better. Third, if your Wii is picking up the modem but not allowing access then this is an encryption issue. Check to make sure that you are entering the proper settings and WEP/WPA or MAC key into the Wii. You can find the "key" printed on the side or back of your router. Also check the router settings as well. Make sure that the router security is set to the proper encryption level (i.e. WEP, WPA, etc.) if your router is set to WEP but you are entering the MAC key it wont work.
Keep in mind the Wii is finicky and in my opinion doesn't like connecting to the internet much. I know in my case that my Wii wouldn't connect to the internet for the longest time and then suddenly it did. I use a Verizon wireless router that is upstairs and my Wii is down stairs. Hope this helps.