If I saw an "untested" monitor on ebay I'd assume that the owner thinks it's broken, but doesn't want to test it for fear of being right. The difference between a working monitor and a broken one can be twice the value. There's reason NOT to test unless you think it's broken. So if you actually get a working monitor out of the deal, you're probably lucky.
As for fixing it, that depends alot on the problem. Some might just be blurry. Others might be fried.