F-Keys Not Working As Expected

I just bought a new wired keyboard (Apple brand, standard alpha w/ number pad, exact replacement for the keyboard that came with the iMac...) yesterday for my iMac. It works as expected in all ways, except that the built-in functions of the f-keys do not work as expected. For example, when trying to adjust the volume using F12, the Dashboard would appear.

Here is what I have already tried to do to troubleshoot this issue:

Accessed the System Preferences > Keyboard & Mouse menu and ensured that the "Use all F1, F2, etc. keys as standard function keys" option was UNchecked. -- was unchecked. Tried selecting the check box and then using the "fn" key with the F12, just to see if it would make a difference, but it performed as might be expected and showed the Dashboard again. (So, unchecked "standard function" + F12 = Dashboard. Checked "standard function" option + fn + F12 = Dashboard as well. Checked "standard function" option + F12 = no functionality at all)

Next, I accessed System Preferences > Expose & Spaces. There I found that for some reason, all of the shortcut preferences for Expose and Dashboard had been reset to F10, F11, F12, etc., which explains why pressing F12 resulted in Dashboard being hidden or shown. I reset these to the appropriate F3 and F4 keys for Dashboard and Spaces. However, this only resulted in leaving the F10, F11 and F12 keys with no functionality at all.

I have no idea how this happened-- I literally just unplugged one keyboard and plugged in a new one. I made no other changes, but my I guess my Mac decided to reassign some keys! I just want the function keys to act according to their icons-- mostly, I want the volume controls and the play/pause, next and last keys to work, and I cannot seem to find a place where I can assign those functions back to their original F-keys.

Any ideas?