Monitor is failing to start although power is on

Sounds like you've got some blown capacitors on the internal hardware of the monitor.

Unless you are a seasoned computer hardware expert or electrical engineer I'd recommend you replace the monitor.

The capacitors that are blown are likely controlling the power aspect of your monitor, and aren't totally defective yet.

Most computer shops would not be able to repair your issue, due to lack of skills related to monitor repair. So you're going to find replacement the easiest / cheapest solution.

Of course you can try to ride out the problem as long as you can. But it will get worse over time.