Personally, I would never consider buying even a used LCD monitor (I'm still waiting for my CRTs to fail), let alone one which is known to be malfunctioning (and has no warranty). I'll amend that...if I were a technician or knowledgeable enough to try to repair it myself, then I might consider it. Only then.
As for hoping that it's something minor...well, you can do that, no harm in hoping. But to assume that you can get it repaired cheaper than buying a new one (with a warranty) and then not have to worry about it failing again...I think that's stretching the old imagination just a bit.
Others here certainly will have different views on what you propose to do.