While the lack of seeing could be the monitor, the fact that it won't stay on and is failing the repair wouldn't be the monitor.
If it is failing to repair when you run the options for recovery or repair, then you need to have it looked at. You might have a failing drive, which better to have it looked at, and get what you can off of it, before the drive completely goes and you lose everything.
If it is under warranty, contact the manufacturer. Just be sure to mention to them about wanting to save your stuff if you can. If it isn't under warranty, then try a local tech.