WHY can't I instal the Mavericks mail update which theoretically will resolve my gmail glitch?

My Mail (gmail) became crammed with all kinds of strange behaviors after I installed Mavericks, but when I tried to instal the downloaded Mail update, I was informed that my hard drive and my external backup were unsuitable for installation of the update. Is my desktop machine obsolete already?

What can I do to make my 21 inch, 2.7 year old 10.9.2 machine (iMac) suitable?