This is a very common issue that can be fixed if your good with a soldering
iron, if you did some searching you would have found it easily.  Please try
searching for "Ford radio display" in google and you will find lots of
information:

http://www.google.com/search?q=ford+radio+display&ie=UTF-8&oe=UTF-8&hl=en

I used the services at the following:
www.shareamemory.com/radio

While I had to pay for the information, it did get me the fix I was looking
for.  I started out checking the rear connection like you did.  I ended up
having an issue with the pins on the front display.  I had sent it of first
for service from someone saying it was going to only cost $45 plus shipping,
come to find out my problem wasn't the "same" problem as everyone else (so
they claimed...my fix was going to cost $175 plus shipping).  I had them
return the radio and found the solution through the above web site, though.
Hope this helps.

I've got a 98 Ford Explorer with the radio/CD/cassette.
The problem is the LEDs that indicate frequency, time, etc do not
work,
so its difficult to determine what station it's tuned to.
They worked intermittently for a while, then quit, so I suspect the
cause is an intermittent connection in a connector.

How can I get the radio out of the dash, so that I can check if the
connector on the back of the radio is loose?

I have a cassette radio,
This auto-reverse tape deck was removed from a 1997 Ford Thunderbird when I
bought the car new in late 1997. I replaced it with a CD player. The deck
was removed while still brand-new, and has been stored indoors in a box ever
since. It should still work perfectly. This stereo should fit several other
Ford models, but check with your local Ford dealer if unsure.

Yours for $40 including shipping