It's likely to have gone south in storage. Use a voltmeter to test it (you don't even have to take it out). Full charge is 3.6 V -- if it's anywhere below 3.0 V, replace it.
Especially if the PRAM battery is dead, you might try letting the PRAM get a "trickle charge" by leaving the computer plugged in for 24 hours, then trying to start it up.
btw -- how are you trying to start up? I've never owned a Color Classic, but I know there are two different methods for Macs of that era:
1) You start the computer by toggling the switch on the back (Macintosh LC III, for example).
2) The toggle switch on the back merely "enables" the power supply, but the Mac is started up with the "left-pointing triangle" button on the keyboard (either a long, flushmounted, rectangular button above the numbers on the main keyboard, or a key sitting all by its lonesome, above and to the right of the numeric keypad). These models might also have a small "reset" button on the back of the computer, near the toggle switch or near the monitor port, which does the same thing as the "left-pointing triangle" button.
Try a couple things, then report back.
Triple post, sorry!
Yeah, I've tried both ways to start it up. I'll try PRAM next.
The proper order: Turn the rear toggle on first, then press the keyboard button.
Try just removing the old PRAM battery completely, re-install the MLB, switch on the back power switch, wait a few seconds then press the keyboard power switch.
Also FYI - the box and original packing materials are probably worth considerably more than the CC itself, so don't damage or lose any of that stuff.
Thanks so much guys. All I had to do was flip the switch and then hold the power button. I guess I never seemed to do it in the right order or hold the power button long enough before.
I've seen this problem before, with some of my (many) CCs, and with other folks' CCs too. For some reason you have to hold the keyboard power button down for a couple of seconds for certain CCs to start up. I've even seen a couple where they never, ever start up the first time you hold down the keyboard power key, but if you let up and then hold it down again, they start up just fine (this is different from the issue where some Macs won't get any video unless you "double clutch" the rear power switch).
BTW: leave the rear toggle on. There is no reason to turn it off unless you are going to unplug the system or something.