Could be;
oldstarter? tap the starter with a hammer near the solenoid, it could just be sticking.
Starter been removed lately? i see alot of " loose starter wire arcs through terminal and falls off " scenerios becuase the nut has " walked off " the pole.
Bad ignition relay maybe??
Could just be to low of voltage to engage starter solenoid. If you have a volt meter, hold it between the positivee and negitive side of the battery, 11.0 volts up sounds about rigth for a cold but fully charged battery. If it comes up low, hold the voltmeter between the neg of the battery and chassis of thecar, if you get a voltage reading at all, something is either still on or grounding out and killing the battery. Then try to check the voltage between the posi side of the battery and the engine block/head with the ignition key turned on, if you get nothing it could be the engine ground like ahhvtec stated earlier