Computer won't release IP address

I am having problems connecting to my internet service.  I called the provider yesterday and she said there are no service issues and that my modem was showing active (lights were all on too!).  I usually use my wireless router, but since I was having issues, I bypassed it by plugging the Ethernet cord directly into my computer.  We went through a bunch of steps including using the ipconfig\release and ipconfig\renew functions and then under control panel – network went through all of the tabs.  She said she couldn’t help anymore and my problem is that my computer is not releasing the wireless routers ip address and picking up the modems ip address.

Any suggestions on what I can do to fix that???  The computer is a Dell Inspiron 8600.