Cox refuses to provide service to my address. Cox is the only cable service provider in my rural area. Homes all around me have Cox service. My home was skipped by the cable company when they laid in the cable. NOW they demand that I pay thousands of doll

How many "thousands of dollars"?  

I would expect it to cost a $2000 - $3000.  

You could get your own quote to:

1) dig a 100 foot trench to a depth of 3 feet

2) lay in conduit (1.5" inch -- but check with Cox for their preferred size). 

3) pull underground rated coaxial cable through the conduit (although check with Cox -- they may prefer to pull their own cable).

If you can get the trench and conduit laid cheaper, I'm sure Cox will work with you to hook you up.