Kernel panic or logic board?
If I understand your question correctly, you've now removed the two 2GB RAM modules and now when you try to start up your iMac, the screen remains black and you hear a sound every second?

This model iMac only has two RAM slots, and since you've removed both modules, it now has no RAM at all. As a minimum, Mavericks requires 2GB RAM installed.

As a starting point, I would re-insert one of the modules into the first slot and try running the iMac to see how you go. If the problems return, swap the modules and test again.

If you get no joy from the above, then try it again with the second slot.

Either way, let me know how you go.