Starter will not engage

Okay, when you shut the door and use the key fob to lock doors. There is a beep and the security light comes on for a few seconds and then goes out. So it appears the security is arming and disarming right. Did not replace the battery in key fob for as it appears to be working okay. Should I replace it anyway?
When I turn the key on I get 2 warning lights (Check Coolant level and fuel level low). Could the low fuel level low, disengage it from the starter working?
Read on net on how to reset the security system (just in case it was not disengaging) and tried both ways that I found on the net but neither seamed to make a difference as starter still will not make a sound. There has prior to this been no indication that the starter was making any unusual noise of troubles.
Thanks in advance for you input. Desmond