Many older computers used to flash the disc drive activation light to indicate an error code, once floppy discs became common and boot processes became complicated enough that they could ever partially succeed. That doesn't seem to be true of the amiga which instead flashes the screen different colours, so if your screen out is knackered you've got very little to go by.
However, the amiga kickstart on an amiga without a hard disc with workbench installed to it should just display a logo and try to boot a disc, be that the workbench disc or a game disc, so the light coming on then going off doesn't sound bad at all (you may also be able to hear the spindle motor whirring). So try a game or your workbench discs and see if it starts loading those. If you don't have them, you might be in a bit of a bind, but USB floppy disc drives are now cheap and blank floppies are still available, although decent brands are now stupidly expensive compared to olden days, and I don't know if you can write an amiga discs using those types of drives actually.
