PS On closer examination, if I run a flat tool from the top to the bottom of the opening to the optic drive, there seems to be some kind of flap just after half way that is stuck. It doesn't move away so there is no way the DVD can get out on it's own. I think this is what is preventing the DVD from coming out. And hence why all the other solutions (and thanks for those) aren't working. The DVD must be coming up against the flap on its way out then heading back in again.
I think QEII Student IT is right. I have decided to purchase the necessary tools and sort it out manually myself. Will change the battery while I am at it. There have been some other answers, like trying with a pair of tweezers, which I may go for in the meantime. But I have more or less decided to jump in the deep end and take matters into my own hands. I think it is the optical drive that is at fault here rather than anything else. The computer seems to want to work properly but the hardware isn't letting it.