Aren't electrical intermittent problems the most frustrating!
Your problem could be any of the faults noted above, or a couple more. See these links for info on the the starting process and by inference, potential faults.
A defective key is possible (actually the security chip in the key head, which by the way is completely independent of the remote lock/unlock buttons.) Try another one for a while to see if the problem disappears.
If you have the skills and a voltmeter, a test probe on the starter solenoid trigger circuit would help separate problems with the starter solenoid/motor itself vs ingition switch/EWS systems.
I've seen a couple of threads describing an intermittent "no starter action" problem such as you describe being caused by a failing ring antenna around the the ignition EDIT: switch not key as in original post. When the ring antenna doesn't read the security code in the key, the EWS module won't trigger the starter to try to engage and turn the engine. The repair was reported to be an easy DIY and ~$50 for the part.
Last edited by rdl; 10-03-2012 at 08:09 AM.
Reason: clarify ring antenna location