Both Minnesota and TCU claim a national title from 1935. Let's examine each team's merits and then fight this one out in the comments.
Four teams actually lay claim to 1935, Minnesota, Princeton, SMU, and TCU. For today's purposes we are excluding Princeton (because they nerds), and SMU (as a retroactive punishment for harboring Craig James #CJK5H). So let's look at the two teams left.
The Argument for Minnesota:
The Golden Gophers ended 1935 with their third straight undefeated season.