First, it's always handy to check out Nintendo's Network Maintenance Information & Operational Status page to see if the Wii U's network is either down or under maintenance. If everything checks out there, take a peek at your Wii U's network connection and make sure everything operating per the norm.
- From the Wii U menu, open the System Settings app.
- From the Internet page, tap the large Internet button.
- Tap the Connect to the Internet button.
- Press X, or tap Connections in the upper-right corner of the gamepad.
- Tap your current active connection from the list.
- Tap the Connection Test button to ensure that you're connected to the Internet.
If your Wii U fails the connection test for some reason, grab another device on your local network and attempt to connect to the Internet. If other devices can't connect, it's your network! Try rebooting your router and try again.
However, if other devices on your network can connect, then your Wii U is probably the issue. Either edit or delete and re-add your connection to ensure that your password, IP, and proxy settings are all correct.
If on the offchance your Wii U passes the connection test but continues to fail connecting to Splatoon, it's probably just the Splatoon servers specifically.