What battery do I use to power solenoid?
Looking at the size of the solenoid: that thing is meant to have a lot of power.
Your battery is not meant to provide a lot of power, at all.
This won't work.
You need a battery with higher current capacity. How much – hard to tell, but maybe the label or definitely the datasheet of the solenoid would tell you.
To test, use a 12 V power supply that is certainly able to drive this (a lab power supply, a car battery, …), and measure the hold current, and if you have an oscilloscope, also measure the turn on current.  Then you'll know what kind of current your battery needs to source, and then you can pick a battery.