I have a 2000 town car signature series. Having issues with it overheating. Hard to crank n stay running at first, but after I drive for a few minutes then cut it off, I have no problems recranking. I will throw out some key issues. Any suggestions will be appreciated. (very much)

-purchased a week ago n had no problems driving it from new orleans louisiana to brookhaven ms. owner was towing company n said it sat up 5 months.
-ball joint was broke, so had to reset fuel pump switch
-new alternator and serpentine belt, battery, thermostat
-EATC self diagnostics test returns no dtc's
-radiator fan does not kick on in low or high, with or without heater or ac on
-jump wire connected from radiator fan to battery proves fan motor is ok
-checked 4 fuses/relays, locations: 50 amp maxi fuse #3 (high speed cooling fan) & #26 which is low speed cooling fan 30 amp in main fuse box under hood . Both were blown so I replaced them. And 2 big relays in small box in between breather and main box, for low n high speed. Swapped relays around n horn still blowed so relays are ok.
-not showing power with test light to 2 15 amp mini fuses in main fuse box under hood, locations #20 (fuel injectors) & #21 (heated o2 sensors, tranny solenoid, evap canister vent solenoid, egr vacuum regulator, evap vapor management valve) . Replaced both with new fuses, test light still wont come on. Is this normal or possibly an electrical issue? 
-hoses from radiator n water reservoir have good pressure, so I dont think it is water pump
-have not saw any leaking hoses
-thinking a sensor could be the cause (coolant)...but which one and how do I test it???
-any ideas/suggestions??????? I have both owners manual n repair guide book, but I am female and am not a mechanic. Lol. So please be user friendly . :))
Btw, check engine light is on, flushed radiator...still samr problem (overheating)



Thank you