problem Reloading Synaptic Program Manager
 

I clicked on reload, it was firts running and later gave this error message W:GPG error:http://archive.ubuntu.com precise Release. The following signatures were invalid. BADSIG 40976EAF437DO5B5 Ubuntu Archive Automatic Signature

Your BADSIG Problem is an easy one. Your signatures are uncorrect.
Update them with:
sudo apt-key adv --keyserver keyserver.ubuntu.com --recv-keys 40976EAF437D05B5

(This answer is copied from first hit on google... ;.) )