Had the notion that that might be a problem, so I checked that the floppy drive doesn't have any disks in it. And also I removed the hard disk just to be doubly sure.
I managed to boot using the command-Option-X-O combination when turning it on (thanks for the tip MultiFinder17). But I wasn't able to do so after I re-installed the hard disk. From the looks of it, it seems that the hard disk might be the culprit, since I hear it running, but I don't think that it's actually functioning correctly. I'll have to find a boot disk for the Classic and try to boot from it (first get a floppy drive for my MacBook to write the disk) to rule out any other components.