Try powering on with the Option key held down to see if you get to the drive selection interface. That's before the OS boots and can maybe narrow this down to a HW vs SW issue.
Not sure what Startup Sound is, which you say you get while also saying you get No Chime. Does it make a noise through the speakers or not?
Couple of other things to check are to see if the Caps Lock key will light the Caps Lock light, that will tell you if it's powered on or off.
Also try shining a flashlight through the Apple Logo on the back of the screen to see if there's anything on the screen and possibly a backlight failure.
But give the model and age, it's quite possible that you've gotten hit with the Nvidia GPU failure that all of those suffer from and Apple was repairing for free for several years.