Look for

.thunderbird 

in your own user folder. It is, of course. hidden.

i.e

cd ~/.thunderbird/ 

should find it.

Best and easiest thing to do is rescue the entire profile - that is, everything at the location given above, and transplant it all to your replacement computer.

Address Book files are stored with a .mab filename extension. They are not very useful as stand-alone files, but could be re-imported into a new Thunderbird.

The calendar's data is stored, I believe, in sqlite format and I can't recall ever trying to dissect these files. I'd just restore the whole profile on the replacement computer. I think there is a Firefox extension which allows you to inspect sqlite files. Maybe it can export the data, but simply re-using your old profile remains the most easy way to go.

https://github.com/lazierthanthou/sqlite-manager

About profiles: https://support.mozilla.org/en-US/kb/profiles-tb About what's in a profile: http://kb.mozillazine.org/Files_and_folders_in_the_profile_-_Thunderbird

My ubuntu 14.04 has gone tits up

What does this mean? And what exactly are you trying to achieve now?

Make sure you can view hidden files and folders and the settings for Thunderbird is usually in say ~ .thunderbird while Firefox and SeaMonkey is in ~ .mozilla

christ1 said

My ubuntu 14.04 has gone tits up

What does this mean? And what exactly are you trying to achieve now?

Either the Ubuntu Linux install or the PC itself had issues so the OP was mounting the drive to try and recover the stuff from Thunderbird.