"and I bought an HDMI splitter so I could capture from my TV instead of my monitor"
Odd phrasing there, I assume you mean you would rather play on the TV rather than the monitor and just leave the monitor/PC to do its thing.
Anyway I would possibly try to eliminate that first -- play with fancy things after you get it working* in the most basic capacity. If you have another device with HDMI out (laptop, raspberry pi, possibly TV box but they might be protected) then bring that to the party so you have other things to eliminate with.
*I say noting many a cheap Chinese splitter just so happens to also remove HDCP protections that some game consoles (not sure what goes for the Wii U, quick search says none used but other things might leave it for specific games/things like netflix).
Never heard of the card and usually do what I can to avoid OBS (it is reasonable for what it is but I don't like it, more of a personal quirk than hard technical suggestion though) so not sure what I can do there. At times OBS can have some bizarre settings that need twiddling rather than being plug and play, especially when it comes to external video sources.
My usual choice for capture devices is either virtualdub or playing with filters directly (don't do that), though virtualdub is ancient and I use it mostly because I know it and know it plays nicely with a lot of older capture cards which is what I tend to be concerned with. You can give it a go if you want as having it display something there might allow you to say "I know the hardware and drivers are good".