Coax for Networking was always 50 Ohm not 75 Ohm as used for TV/Radio signals. Network Coax also used BNC connectors with T Pieces at every computer. I haven't seen any of the T Pieces around recently but then again I haven't been looking either.
If you have 50 Ohm Coax you can get an old Hub/Switch with both RJ45 & Coaxial connectors on it from a place like E-Bay or any other second hand Equipment Supplier. However this will be much slower than the current 100 T Base installations that use CAT5E cabling.
But if you only have one or a couple of terminals this will work but when it breaks you'll have to hunt around for more secondhand equipment.
For a better coverage from the WiFi you could use a Range Extender like this one
http://tinyurl.com/2yrapj
Or you could use one of the new Networking gizmo's that turn the Electrical Wiring into a Network Connection. Not sure who makes them but I do know that you need to stick to the same maker for all the bits or if you need to add another station.
While too slow for business I understand that they are OK for home use and much cheaper than installing CAT 5 Cables.
Col