Computer turns on but no picture showing on monitor

I have a home built computer, it turn on the light is green, fan running but nothing's showing on the monitor. I've tried holding the button down for a good minute and plugged everything back in and it's still the same. At my old home it worked fine and I know all my cables are good as well as monitor. Just don't know why it's not wanting to turn back on. Did put a new hard drive in it though but I tested it out and it worked right before I moved. I'm not very computer savvy so any help would be greatly appreciated.