"Powers up, blank screen" covers a whole multitude of possibilities.

If it's a digital scope then I'd expect something on the screen. Even if the trigger is set and untriggered there would generally be some configuration/setting data displayed. If not digital, at the cost of scopes these days I wouldn't entertain an analogue scope.

If it's a CRT (rather than LCD/TFT) then it could be as simple as the brightness turned down, but that's rather a bit too hopeful I think.

I'd tread carefully. How much cost and effort are you looking to risk on this (i.e. "free, around the corner from you" is a bit easier to swallow than "200 quid and 200 miles round trip"). If you want a second pair of eyes (I've rejected driving from Lancashire to Devon, btw), and can share details then feel free to PM without any motive on my part other than to offer help.