Now reattach the battery and retry the El Capitan installation one more time. Now lift the battery a bit, remove the connector from the logic board, press the Power button and hold it down for 10 seconds with the battery still disconnected. Locate the battery, then remove the three screws to detach it from the logic board (two screws are in plain sight and the third screw is hidden under a warning label.) To do this, you’ll need to remove the screws from the bottom case, lift the case just like you did back when you installed the SSD. If the installer still crashes during logBatteryState, try resetting the system management controller by physically removing the battery from the logic board. (Source: Reset SMC of a MacBook Air, MacBook Pro Retina, or MacBook Pro’s with an internal non-removable battery)

The MagSafe light should change colors for a second or so if it doesn’t, retry until it does. Keep an eye on the little light on the MagSafe plug while you hold down the for keys. Your Mac needs to be connected to a power supply during that entire process. Shut down your Mac one more time, then reset its SMC by pressing ⇧ Ctrl ⌥ and the Power button at the same time. Make sure to hold the buttons until you hear the startup chime for the second time. Second, reset your NVRAM by turning off your Mac, holding ⌥ ⌘ P R and turning your Mac on again. To fix this, first be sure that you are not only connected to the mains but also have a working battery actually attached to the logic board of your MacBook Pro.

The fact that this fails is indicative of an issue with the battery of your MacBook Pro. The installation fails due to a crash caused by the SystemMigrationUtils process while it tries to talk to the battery of your MacBook Pro: Jan 27 11:29:21 Thread 8 Crashed:: Dispatch queue: -qos

Upgrade from snow leopard to el capitan