Why do you use an adapter? Assuming you have a router surely your wii can connect straight to it?
As for firewalls you can set-up specific access for devices or alter your security settings to something like WEP (lower security but still provides a password).
Quote:
Allowing TCP and UDP Traffic:
The Wii console may require unrestricted access to several sites across various ports and protocols to function correctly. These addresses and ports vary, and may change in the future without notice. Many software firewalls restrict outbound access. Only if your firewall blocks outbound traffic do you need to enable this traffic:
TCP:
Allow traffic to all destinations on ports: 28910, 29900, 29901, 29920, 80, and 443
UDP:
Allow all traffic to all destinations. (Necessary for peer-to-peer connections and game play). Our Network Test tool can be used from a computer behind your firewall to test if outbound UDP is allowed.
|
Source:
| Nintendo - Customer Service | Wii - Firewall/Antinvirus/Antispyware/Adware Compatibility Info
Opening up those ports may help with random disconnects as well. Good luck and hope you get it sorted. (again without seeing the PC and Wii it is hard to be helpful any further)