I set some to-do reminders in Korganizer but they don't seem to work when Korganizer is closed or open.
I do not get the reminder message or sound.

It works fine for me. I remember I struggled a little the first time.
If that can help this is how i configure my Korganizer:

1) On settings-general I have unticked the "use email settings from system settings"

2) Just below that I put my name (or nickname) on "full name" setting

3)Then I inserted my email address on the below section

4) On "default email attachment method" I have ticked "attach complete message"

5) When I put a meeting or a due date I, obviously, double-click the date that I need. On the new window I put the title, in the middle big section
all the info that I need. On the little menu above it I click on "reminder"

6) On "default reminder" i choose when I want to receive the reminder. Let's say "2 days before start" and click on ADD.

7) Highlight the below new entrance (in this example "2 days before start"), then on the right menu select "modify"

On "what" section i choose "send email"

Always worked with me this way. Let me know if that helps

I tested the reminders some more. When I set a reminder to go off a minute from now it works but when I set it to go off at an hour later it doesn't work at all.