Robotoer, the coax cable that is in your house is likely TV cable, that is, RG59 or RG6. Both of these cables have a characteristic impedence of about 75ohms. 10Base2 / thin Ethernet uses RG58CU, which has a characteristic impedence of about 50ohms. That is to say, there is an important electrical difference between TV coax cable and thin Ethernet coax cable, and equipment intended to be used for one will not work with the other.
You can verify the cable type by looking at the markings on the jacket of the cable. Look for RG<x>, and likely values are 58, 59, or 6.
If your cable is in fact RG58CU, then hit Ebay for thinwire Ethernet products. In particular, I would suggest you try to find 10BaseT<->10Base2 transcievers, if such beasts exist.