It shows the network as public.
"I can get on the internet the whole time"
Could you be bouncing to a different wireless network? Are you broadcasting your SSID and are you using security - do you have any other wireless networks in your profile that it could be connecting too?
if it is bouncing to different network, this would explain loss of connections to your devices but still internet, etc.
I had this problem with my laptop also.
I restarted the laptop with the wireless connection switch shut off.
After reboot was complete, then I turned the switch back on.
Then open control panel, Network & Sharing Center.
Should be your default network now & private network status.
Across from that click Customize.
At the bottom of the pop-up click 'Merge or delete Network Locations'.
In the pop-up if there is a Network that is not in use delete it, then close/cancel the remaining open windows.
I have a third party software firewall (Comodo) installed on my laptop which I use and thought I had the windows firewall disable but I guessed wrong.
So I went to start menu, control panel, windows firewall, and found that even though I had it turned off it was still monitoring my system.
To disable the Windows Firewall on a network connection:
1. Click Start and click Control Panel.
2. Click then select Windows Firewall.
3. Click Change Settings.
4. From the window that appears, click the Advanced tab.
5. Remove the check beside the connection that you want to disable the Windows Firewall for.
6. Click OK.
Then from the start menu, run command, type 'services.msc' without the quotation marks.
Find windows firewall, highlight and right click, then click properties.
At service status click Stop.
Then from the 'startup type' drop down menu click 'Disabled'.
Click Apply, then OK.
Reboot, all should be fine now.