I just spotted your post with the battery specs. Way too small. To get 12VDC, 0.5A (6W), to allow for the wrong ratings on that monitor, the DC-DC converter will need to pull in excess of 7W at 5V, about 1.5A, at 85% efficiency.Here are some more clues that may help. On the battery it says-
Input 5V/1A Max
Output 5V/1A Max
Capacity: 8.14Wh(2200mAh)
http://www.amazon.com/Color-Cube-Portable-Power-Black/dp/B00KPXZPWA/ref=pd_sim_sbs_86_1?ie=UTF8&refRID=08ET99PWMG20WT1BC56B&dpSrc=sims&dpST=_AC_UL160_SR160,160_
To run for 1 hour, with a current drain of 1.5A, it would require a battery of over 15Wh, (3000mAh), and probably nearer to 20Wh, (4000mAh).
Those battery specs that you posted don't add up, either. 8.14Wh at 5V is 1628mAh.
So, you'll need a much larger 5V battery and a larger DC-DC converter.