There are two different chumby Classic devices with different screens - the 3.7 and 3.8 devices.  You can tell the difference in two ways - 3.8 device power on when connected to power, and have variable screen brightness.  The 3.7 devices require you to hit the power button and only offer a single "dim" brightness level.

In general, it's tough to replace a Classic screen, because it's basically soldered to the main board.  It can be done with a lot of care.

We don't have any spare screens that are not already attached to boards. I'll see what I can find in inventory.

Opening a Classic is tricky - you have to carefully pull and cut away the glue holding the hard plastic bezel to the soft plastic.  If you take your time it can be done cleanly, without distorted or tearing the softer plastic.  I've done it many times, but it takes patience and care.

I have the Chumby disassembled. Is there any one failure mode that would prevent the unit from powering up? The speakers make a "click" noise when the power switch is pressed but the screen never comes to life.