Short answer, clean and reseat your ground cable and any other termination points you can....probably worth doing the positive side as well.
Long answer, after doing my timing belt I got the motor to crank, start and died. After that I was only getting a click like you. I turned the motor over, determined there was no mechanical issues. After multiple attempts to jump start and alternate batteries, I replaced the starter, NOT A FUN JOB!!! (what brilliant engineer decided to jam the starter under the intake manifold and bury the bolts up against the firewall?). Anyway, with the new starter the result was the same. Only after cleaning up my battery terminals (which did not appear bad) was I able to get it to crank again. If at first you don't succeed, keep checking terminals and connections.
For the record I kept the new $100+ starter, no way was I going to do the starter replacement labor twice.