If your battey is good, and your soloniod has just been replaced even with poor cables and connections your starter should at least turn the motor over slowly, unless its the starter itself.
if your ford starter motor is the older movable poleshoe type, which doesent have a additional soloniod on top like the newer ones, then i would say that chancer are good that the pull in windings inside the starter motor are possibly at fault, if the windings were working you would still hear a additional noise at the starter even if it didnt turn.
if its a non solonoid type starter just put a jumper cable straight from the battery carefullyto the starter motor,(leave ign. off)
if it doesnt crank, then connect the other jumper cable to the neg battery post and starter motor body, if it then starts check the starter motor ground. if it doesnt crank at all the starter is faulty, if it does jolt or make any clunk noises, but doesnt turn over, check to see if you motor is not seized, just incase.
Turn your lights on, if they dim totally when the engine is crank is attempted then the starter could have a short, if they dont flick ar change at all, the starter could then have a open circuit.
usually a clutch safety switchfor a standard trans, or neutral safety switch come before the solonoid, so if either of those were at fault, the solonid would not even be heard.