If you are on Windows 7 like me, they are stored at C:\\ProgramData\\Origin. This is a hidden dir by default so you need to unhide it (if you don't know how, repost, will tell you, else assume you know). Delete all the files in here. Before you do, make a copy of the dir, then rename it to say
Origin.OLD.
You can also try uninstalling Origin. (Download it here
http://www.origin.com/download unless you have it already)
I've just upgraded computer so reinstalling everything and getting ME3 working again (yeah right!!). I'm not sure if uninstalling it deletes these files. So try it and see. Do a System Restore first. That way if anything goes awry you can get back to where you were.