Okay, since I didn't get a response, i'll try asking a more specific question:
I'm interested in building a handheld/slightly-thicker-than-a-tablet-size PC for playing games in 720/1080 on the go (rough build: http://ca.pcpartpicker.com/list/2VCpBP) and was wondering about powering such a device with a rechargeable battery. Would this be possible and if so, what battery could be used (I found this one for about $25 but I don't know if it would be powerful enough to run such a device for 2-3 hours plus the screen)? As a follow-up, would it be possible to solder button inputs to the motherboard? Budget is $1,000 but i'm willing to spend a bit more efficient components.
Define "On The Go"? I don' think this is going to do what you think it does. That battery is 12V and at 6800ma it would only last like, 25 minutes, if that.
Why not just get a Windows 10 Tablet?