QoS does NOT block your computer from getting internet access, and priority does NOT work that way. Your setup was probably done by someone with zero knowledge of networking and should be redone from scratch.
Here's the steps:
1) If you have a router and modem separate (which you should), turn off wireless functionality of the modem and use only your router
2) Grab the manual for your router and read it thoroughly
3) Reset your router to factory defaults
4) Add a new password to the router
5) Set up wireless, using a proper password
6) Check to see that everything works