I have assignments showing to be graded on my To Do list, when I click on the assignment it takes me to Speed Grader and shows me a student without a submission. In fact there are no ungraded assignments. These assignments have no due dates.
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Because of the particulars you already mentioned here (things showing on your to-do list, not showing in speedgrader, and having no due dates at all), I think this is likely a case to contact Canvas Support about so they can look at the details and figure out if there may be a bug or something else going on here. Users in the global community here can't access your exact account or Canvas instance, so for an issue like this it's hard for us to provide much guidance ourselves.
I spoke with Amy in support. From her comments I was able to see that the Speed Grader has a section choice in the drop down menu of students names. The student who had submitted an assignment didn't show up when I clicked on the To Do list "Grade . . ." entry because it doesn't automatically switch the Speed Grader to the section that a student is in. By selecting "Show All Sections" in the flyout menu on the drop down menu of students names), I was able to see the assignment that needed grading.