do all coax cable run internet in the house?

I have my main cox box/cable modem in my downstairs living room. I do have an additional receiver in my upstairs bed room. My question is, can I run internet off my cox box up stairs? Id like to plug in my laptop using ethernet somehow using the upstairs cox box if it provides intternet.

I guess maybe a better question is, does every coax cable also run internet? I was hoping to plug in some type of device into the cox box and then run eithernet off of it. 

Not sure if all coax cables in the house run internet as well?