How can I fix my window washer?

I have a 1999 1.6 Renault Clio and for some reason the washer has just stopped working. I've tried poking the jets with a pin to no avail. There isn't even a dribble coming out. I've no idea how to get to the bottle because there's a plastic shelf type thing in the way that the window wipers are attached to and I can't see how to get one of them off.

I've read a few people say to make sure the pump is working: when I pull the washer lever, a whining noise is heard, like a motor whirring.

I've also read a few people say to put some vinegar/de-scaler/Cilit Bang in the water bottle, but if the water level isn't going down, how will that help?

I really appreciate any help as my MOT is due in a couple of weeks and this is an instant fail!