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I'd say you did a little homework already there. I would be suspecting a bad LCD inverter also. No doubt you've already seen what is involved in replacement (if not youtube is usually a good source). It's not an expensive part (usually) nor a hard replacement (usually) and as good of place as any to start.
I don't think that is an absolute rule. The inverter is what gives the screen it's power, dim may mean the inverter is going bad, a quick flash would imply an over-voltage shutdown (in the inverter hopefully) or short.
But, the inverter is cheaper and easier than replacing the screen. It may be that you'll end up replacing the screen but I'm simply suggesting the cheaper, easier route (the one I would take first).