Right, so first of all: haven't eaten dinner is the present perfect. Not the past perfect. You don't really use yet with the Past Simple - I believe in America they sometimes do. The basic reason for not using the Past Simple and yet is that the past simple means something is done/finished whereas yet refers to something that is not done but will be in the future. So, the correct phrase here would be haven't eaten dinner yet

In British English 'I didn't eat dinner yet' is incorrect. 'I didn't eat dinner' is ok, and is the past simple tense. It's talking about an event in the past that isn't connected to the present. 'I haven't eaten dinner (yet)' is OK - it's the present perfect tense. You still need to eat dinner this evening but it hasn't happened yet.