'Allo Gary, I am the least techy person on this forum !! that's just a warning
.........
but a friend of mine had a very similar problem quite a while ago, the laptop would not start on the battery, but OK on the mains. They were told to try this ..take out any cords, take out the battery and hold the laptop upside down and hold the power button for 30 seconds, next, turn it right side up and put the cord back in try to turn it on then put battery back in ... et Voila !
I'm sorry that's all in capitals, but it was typed like that on the e-mail I have ....
Amazingly it worked for my friend ....
it does for you too
(edited because I found a very clever way to change Higher case to lower case ! - and didn't want to appear to be shouting
)