Maybe if Giuseppe Zangara hits Roosevelt during his assassination attempt, and Garner promptly mucks things up even more during his time in office (he wasnt to supportive of the New deal, so not too implausible). There would be a lot of variables (Roosevelt's possible image as a martyr, does Garner run, etc...), but Landon might be able to win if the Democrats have failed miserably since 1932. On the other hand, with four years of butterflies GOP candidate (Borah, perhaps).
One other interesting thing to note: At the time the assumption was that the race would be close and Landon had a shot, which in hindsight turned out to be ridiculous. If the depression is not such a clearcut issue for the voters, a fair number may swing back to the GOP.
Finally, a note about Roosevelt being dead. In 1936, roosevelt repealed the 2/3rds rule at the democratic convention, weakening the southern wing's control over the party. It is doubtful that Garner or anybody else would have had the desire or the influence to pull that off. What happens if Southern control over the party is extended for the next several election cycles, especially with roosevelt absent?