A voltmeter is your best friend.....
Attach the voltmeter to battery(I think you said you disconnected the battery cables, checked for corrosion, and reconnected)....on a fully charged battery, you should get 12.6 volts, with nothing on.....
Now crank the vehicle over.....voltage should not drop below 9.6 volts....if it does, the PCM will not function......
It probably would be wise to check your battery cable ground connection....also check the pos cable connection at the starter solenoid, and also the purple wire connection at the starter solenoid "S" terminal...
Other possibilities, if not battery or alternator, are ignition switch or Park/Neutral switch(try shifting into N if it won't crank over in P).....You can check this by checking for BAT voltage at the ""S" terminal of starter solenoid with the key in the crank position...