Power C33 x4 with power supply

Hi, 
I am trying to set up a vstarcam C33/C7833x4 on a car battery and solar panel as I have no power supply in my location. 

I have tried a few different ways converting from 12v and 240v to 5v, but i cannot get the camera to power up normally. The IR turns on a little, but it does not power up, ptz does not start and it doesnt record.  The original power adapter says 5v 2000mA output.

I have tried 
1) using a 12v to 5v 3 amp converter
2) using a 12v to 5v 2 amp usb connection
3) using a 240v to 5 volt, 1 amp, 2 amp and 2.4 amp, 3.6 amp usb connection

Nothing seems to power it up normally. Every time I use the original power adapter, it works fine. 

Is there something I am missing? Why does the original 5 volt 2 amp adapter work perfectly but not when you use equipment with the same output?
Please help, I am going crazy here! Haha

Thanks Teddy. Yes, I thought the same thing. That's why I used a 2.4 amp and then two 1.8 amp usb chargers in parallel (3.6amp) but I still got the same result. Most of my attempts are using a usb to barrel power connector.
I used a multimeter to check currents and voltages, in most cases. The original power supply is actually 5.2v. Could that be the issue?
I have used a Vstarcam C7824 with usb and chargers from 12v and 240v and it works fine

sorry for my english

try with a dc to dc converter step down voltage regulator module

Dear Sir/Madam,
Please use the power adapter in product package.