Unable to Perform Name Resolution
It sounds like the MacBook connection problems only happen when you have blocked the kiddo's x-box, correct?
Does removing the X-Box block allow you to connect to web and email?
If so, the problem is likely happening because of DHCP.  DHCP means the router hands out IP addresses.  Usually, DHCP will hand out IP addresses in the order that devices connect to the router. 

For Example:
1st - 192.168.0.1 -> MacBook
2nd - 192.168.0.2 -> X-Box  [BLOCKED] 

Now lets say the kid reboots the router while you are away.  Now the X-Box connects to wifi first and gets the first IP address. When you get home you get the second [blocked] address 
For Example:
1st - 192.168.0.1 -&gt; X-Box 
2nd - 192.168.0.2 [BLOCKED]-&gt; MacBook  

Setting up your MacBook with a manual address (DHCP with manual address ) might work... but only if you chose an unused IP address in the &quot;proper IP address range&quot; for your router.
If the above is similar to your situation ... The solution to this depends on the make and model of your router.
My router has an option for &quot;DHCP with reserved addresses&quot;.  This will reserve and assign a specific IP address to a specific device.Example: 192.168.0.8 -[BLOCKED] [RESERVED for X-Box] .
The &quot;reservations&quot; are based on a device's &quot;MAC Address&quot;. The &quot;MAC address&quot; is a unique &quot;serial number&quot; for the for a devices WiFi or ether (MAC address is nothing to due with MAC OS.)
Another option is to set the IPs manually but this would could be a pain... There may be other options depending on the make and model of your router.
Please let us know more about your router and router setup.