You have to slide something to allow it to disconnect...

"... The stock cable harness uses a multi-lead connector with a slide locking mechanism. To detach the connector from the old radio, slide the locking mechanism to the side and then the connector lifts off the back of the radio."
http://www.eabjr.com/Business-Radio-C33-and-CD43.php

"... you need to remove the harness from the back of the cd unit. This is a bit tricky. As the diagram on the harness shows (see two pictures down, with the blue wire tap), put a screw driver in the top to loosen it. If yours is easy, it will then slide right up, and you can remove the harness. Most take some monekying, though. I had to flip it over and press on either side of the plastic bracket with a screw driver, alternating sides, in order to slowly jimmy it loose."
http://www.davidparis.org/coupe/hktp.html

 

Video showing removal

I found this earlier today while working on my radio. It seems to help since it shows sliding out the connector. https://www.youtube.com/watch?v=26A4Qt_U_BA

 

The trick is to stick a screwdriver between the the connector and the radio chassis from the REAR....simply lift up on the screwdriver handle and it will pop right off...if you do this from the front you will spend all day trying to get it to disengage...

 

Great advice advice. I'll try this out tonight when I get home. I was just too timid and didn't want to break anything but it looks like it just needs some solid pressure to pop it off.

 

Took quite a bit of upward force but it disconnected...undamaged too.
Thanks again for all your help.

Now, sending the unit out for some rehab.

 

It takes a bit to remove the harness. Put a shot of electronic cleaner on it before you reassemble it. It helps if you should have to remove it again.

 

What Zeeboy said above worked!! I just upgraded my radio and the same exact problem happened to me. The harness moves up above an inch and just seems to be completely stuck, and I pulled and yank as much as I could, doesn't budge. Until! I stick a wrench / screwdriver from back to front (kinda like stabbing myself), with the screwdriver tip pointing to the middle of the radio, and just lifted the handle and the thing came right off.