The other day my 2003 2.5L x-type (auto - 63k mi) started having starting problems. When I turn the key all the lights come on normally and instead of the starter turning the motor all I get is a clicking noise. After turning the key a few times the starter will strain and then start the engine. The motor runs perfectly. A few other issues showed up the same time the starting problems started:

1) The "Sports Mode" on the transmission console will not go on and
2) The door locks will not lock as it normally does when you start driving.

Everything else seems to be working just fine. No check engine light has come on. I have checked the battery (full strength) and also terminal contacts (cleaned). I have also checked all fuses and made sure that the fuse contacts are clean and making good contact.

Any idea what could be going on?