Your capacitors look fine, to give you an idea, this is how bad capacitors would look:
These are bad enough they could cause problems, if they're leaking then they're definitely dead.
As for your problem, it's hard to tell. Monitors aren't very serviceable in most cases, replacement parts being hard to source and replacement monitors not being too expensive. Without knowing more about your problem and the age of your monitor, it's hard to say. A few options:
If your monitor turns on but is extremely dark, to the point you can't actually make anything out, it's possible your backlight or inverter has failed.
If the power LED doesn't even come on, it's possible the power supply or mainboard for the monitor has failed.
Either way, it's unlikely to be a simple fix and as stated, your capacitors look fine. I would opt for just replacing the monitor.