92GT5spd

Ok,heres my problem.......my 92 mustang is giving me problems when I go to start it.Sometimes it starts fine no problems.Other times,I go to start it(interior lights and dash lights do come on),.and it just clicks then nothing.I've replaced the battery,the alternator,the starter solenoid(twice,just to be sure),aand the starter.Now if I pop the hood open,and tap the starter solenoid,all the lights come back on,and it starts right up.Any ideas?Also,I noticed there is some corrosion building upo on the battery leads,I cleaned them with a brush cleaner,still having problems though.