Over the years, I've seen how people have gone from wired to wireless. I can understand the appeal, but the issues of security remain. Even though encryption is used, it takes time for the password to be cracked and the victim's service to be used and abused.
NY case underscores Wi-Fi privacy dangers
Not passwording a wireless router is asking for trouble, and quite a bit of it. If you can't seem to set the password, then TURN OFF the wireless part or ask for help from someone who has done it. That plus change the password of the router. The major reason an open access point is found is due to those who wardrive. Meaning, they look for access points, whether encrypted or not, by way of walking around, driving, or using a bike using something like Netstumbler. When I last wardrove about 2007 for a report for class, there were around 1700 access points. A little over HALF were encrypted!
The second reason is that there are websites that list default passwords for every router made. So if the router password isn't changed despite the wireless being turned on and encrypted, trouble can still happen.
In short, when a wireless router is used, either turn off wireless or set a password, and a good strong one, including the login password. Wired is still quite secure.