Mac Mini folder with question mark at startup the shuts off
I have a 2006 mac mini that is booting up with the folder and question mark symbol and then it automatically shuts off after a few moments. It won't allow me to boot from startup disk. When I hold down the C key the disk utility does not load and then I see the folder and question mark. When I startup holding down the Option key, I do not see the disk as a drive--either way it shuts off pretty quick. I have tried about everything and am out of ideas. I know I need to probably reinstall the OS but I do not have another Mac to run target disk mode....Any ideas?
Mac mini