It depends on the kind of screen it is. If it's a backlit LCD panel (the digits would seem quite "flat" but with sharp edges, and not massively bright) then it could just be that the backlight bulb has blown. Fiddly to get to but cheap parts.
If it's a gas-discharge display (like a tiny plasma tv) then the digits would glow brightly with slightly fuzzy edges. A complete failure of one of these is likely either damage to the glass envelope around it or the high-voltage circuit has blown. Neither of those is going to be cheap to fix.
Or, in either case, it could be the screen driver electronics that have failed. Again, this is not likely to be cheap to fix.
You can still find little shops that can repair tvs, stereos etc although they're thin on the ground these days. Sadly, modern consumer electronics isn't nearly as repairable as the old stuff was
Thanks Snorbs. I am useless at this sort of thing and sadly so is DP. Think it is a backlit LCD panel but I may be wrong. It looks like my radio is now going to be a magical mystery tour from now on. Its bloody typical because on my last one the CD system failed but the radio is still perfect. If only I could just merge the two together... Any idea where parts might come from?