1993 Apple Color Classic
Our "Cousin" has a number of good suggestions.

The "BIOS" which is just the firmware of the machine and not strictly speaking a BIOS needs to be there and non-corrupt just like he said.

You do need a battery and it needs to be good, it won't boot without it. That is what I would replace first. Just pop it out of the machine and take it to a batteries+ store or some such near you. They can test it, if it's good there are other (potentially more serious) issues. If it is bad, buy a new one.

Once installed just try switching it on.

If it is STILL not working it could be a bad power supply or any one of a hundred (literally...) other things. And depending on how much money you want to spend and how good you are with a multi-meter and some Googling for sites with repair info, you might get it up and running.

JUST ONE THING THOUGH It is very important to be very careful working in one of the all-in-one Macs with a built-in CRT like the Color Classic.

There will be a big red wire going into a rubber "boot" attached to the back side of the CRT. Stay away from that, there can be enough residual voltage stored in that tube to kill you. And no I am not exaggerating or just trying to scare you. Stay away from that wire, especially where it connects to the tube and the other end in the power supply. I have worked on a lot of old style all-in-one Macs and you can safely work in them. Just be careful and stay far away from that wire.

If a new battery did not do the trick, I would disassemble it: Motherboard, drives, RAM, etc. (but stay away from the high voltage power supply and the big red wire. Clean contacts and look for capacitors that have swelled up, broken wires or scorch marks. Re-assemble and try again.

That should at least get you started...