This green light would be the monitor power switch ?
Not sure about the peep sound but it sounds like that might indicate a physical failure with the PC to me.
Turn off, unplug, leave for a while, then replug and turn on again. Still a problem ? Check the cables from monitor to PC graphics card, wriggle them about, or plull out and check for bent pins. Still a problem ? Probably needs an expert then, to isolate the issue. If you have another PC you can try the monitor on that to check if the issue is the PC or monitor. Or try different cables in case that is the issue.