I have the Denon Personal Component System UD-M10, It is a mini size and includes a tuner/amp, 3disk CD changer, and a bi-directional cassette tape player. It was bought about 2001. The CD changer stopped pushing out the trays. I can hear the motor turning, but nothing happens. I have 2 CD's trapped inside. I suspect a broken belt or gear.

Hi,
Your suspicions about a broken belts are probably exactly right.
Here's what you can do or attempt to do.
Make sure the machine is unplugged.
Remove the cover of the unit. You may be able to manipulate the cd changer mechanism so that you can replace the belts connected to the door mechanisms. Since I am not there and I don't know how your unit is constructed I would advise to be VERY patient and exacting while doing this.
DON'T FORCE ANYTHING. And use good lighting so you can observe how it functions.

I have replaced a lot of belts on various types of CD transports and there is a certain similarity they all have. Inevitably they all have some small belt that rotates a gear mechanism that moves the transport drawer or section in and out.
Of course you can get it serviced by a professional, who will do as I suggest. But if you are confident that you can do it. Have at it.
The only problem I can imagine is locating an electronics supply house in your area.
You may be able to get a full set of belts from Denon.
I hope this helps you.
Best Regards,
Mark