Larger comment sorry :)
So...That's some serious bad corrosion you have in the battery connection, and I suggest redo them with new clamps and their respective screws, also clean the battery terminals with a wire brush, ideally the ones that have the wires inside a hole, so you insert the brush in the pole and turn it left and right for clean up. Like this one http://www.etrailer.com/static/images/pics/D/W/DW00254_2_1000.jpg Connections should be pristine.
A battery can read 12 VDC, even 13+ VDC and however have not enough amps for the strong twist the starter demands, or just too weak to maintain the charge for a starter. It may charge, but at the first super-consumer attached, it will weak out.
However, if you jumped and still no crank, hear the starter how it sounds:
- Nothing means current is not hitting the solenoid, check wires, check
fuses, check if current is reaching the solenoid. Maybe the connection there is also corroded
- A click sound means current hits the solenoid but it is not connecting the
motor: bad solenoid, change it
- "Hum"sound, like if the motor wants to turn but can't: seized motor, probably bearings are damaged, change it
Of course, you can adventure and take the starter out, do some tests and maintenance work and have it back working. Not complex, but you need to have some skills.