At the top right of the Thunderbird window, click the menu button > Options > General > When new messages arrive:

Check 'Show an alert'.

the notification does pop up now that I did what you suggested but it STAYS ON until I "x" it off. It seems to last for "335 seconds" which is the default and although I try to change this number it keeps reverting to it. Thanks for your help

How exactly are you trying to change the number?

In case it isn't obvious, there is a 'Customize' button right next to the checkbox.

I try to change the 335 in the customize window but whatever I do it stays at 335.

Can you explain 'but whatever I do' in more detail?

All Ok and working now. Thanks for your help and patience!

For the benefit of others, what did you do to fix it? Also, when your problem is fixed, can you mark the thread as 'Solved' please? Thank you.

I just followed your instructions. I missed "un-selecting the number 335".