Quite possibly.

It would help to know if the screen shows anything on start up or if it remains blank throughout.

If it is the latter then it is probably just the screen as suggested.

Sorry I'm crap on computer stuff. What is this repair disc?

If your screen is totally blank throughout the start up process then the screen itself is likely to be the problem. A recovery disc will not help in that case.

You can replace a screen yourself but if you are not experienced in fixing hardware then that might not be for you.

If your priority is to recover files then follow the advice given previously and connect to a separate monitor or remove the hard drive and connect it to another device. Sometimes the drives are easy to remove but if not, see if there is a Youtube video guide for your make and model.

For price competitiveness and speed of delivery, check out eBuyer.

Quite but a Chromebook with Linux Mint or something would be ok for most

From what you have previously said you requirements are not that demanding, surf the net, store images, so pretty much any new laptop will be fine. Most of them come with a DVD / CD writer.

You only really need to worry about quality when you have specific requirements such as gaming where you would need a proper "gaming chip" for the graphics. So if price is the real driver shop around for the cheapest option and don't worry about the brand name, technology is pretty reliable these days.

If you intend to store lots of pictures I would suggest you buy an external hard drive which plugs into your laptop. You can pick up a good one for £50 with lots of space, this means you don't need a huge hard drive on your laptop although most seem to have that anyway.

One more point