updated to OS X 10.9.3 and my mail ad other apps no longer open. The error message says that they are old versions which need to be updated. Seems they need to be moved into the applications folder but I cant do

Yes I do have a WD MyBook for Mac backing things up.

I have tried your suggestion about making a duplicate which allowed me to move the duplicates of the affected apps into the applications folder.. I have renamed them as Mail 2 etc (I cannot rename them to the original names because I still have the original apps in the applications folder, so should I move those temporarily to the trash folder)? I have tried restarting and searching for updates but the message says that none are available.

Sorry about the delay getting back to you. The other apps are working fine now thanks, only Mail will not open.

I seem to have two versions of Mail, one appears in the apps folder in Finder. This contains 53MB and was created on 25 April, ie before I updated to 10.9.3 and I think I must have recovered this using Time Machine. This is the normal icon (ie it is not greyed out and does not have the circle and cross on it). What seems to be another version of Mail is now in the dock only. It is also normal in appearance but has a '2' in a red circle and I don't get a drop down list if I right click on it. So it seems that I have two current Versions of Mail but the problem is now how to open them.

Oh yes , my brain fade, no wonder that little 2 was familiar!

I have got Find Any File and using the procedure you suggested I find there are 2 versions of Mail. One was created on 25 April 2014 and contains 32.3MB and the other was created on 28september 2012 and contains 26.8MB. presumably I need to get rid of the older one once and for all by emptying the trash, then how to open the newer one?

The only path I can get for that one (by right clicking on the Mail app in Finder , opening get info then dragging the text under the keyword "where" into a terminal window) is /Applications/Mail.app which presumably doesn't help much.

Nothing happens if I double click on the Mail icon but if I press control then mouse click I do get the drop down list -Open , Show Original, Move to Trash etc. However clicking on the items in this list has no effect

Yes , in the dock and I am gearing a chime and seeing a box pop up when new emails come in , the only problem left is that I can't open Mail

Thanks for the suggestion, I had done this earlier and it fixed the issues I had with apps other than Mail (not sure why that was different) , anyway everything has come right so I am happy now

Thanks for this, Mail has mysteriously reappeared and now seems to be working fine. I can't fathom why the various fixes we tried didn't sort it before but when I logged in this morning it opened fine. I appreciate your kind help on this one