The initial "chime" sound is generated in software when your Mac passes the Power-On Self Test. If the chime occurs and/or startup continues, your Mac is working. The screen should light up and draw a blank gray screen. Then on to the Disk Drive.
if you see a blinking power indicator light instead, that is a "help me" message. Report what number of blinks you see for assistance.
NO chime and no "help me" message suggests the processor in not even getting going.
You may not be able to get this computer running well enough to make backups in the usual way. But if your drives are in the SATA drive bays, they can each be removed and placed in a SATA/USB enclosure or "toaster"-style non-enclosure, or even a naked cable-adapter to make a copy of whatever you want.