You can splice RG-6 to RG-59. They both take F Connectors (the standard CATV screw on we all know), the only differnece is that you have to get the connector for the type of cable you are using. A RG6 connector will have a larger barrel in the back, but the part that screws into your TV is the same as that on a 59 connector, or even an RG-11 connector. in your case, just crimp the appropiate connector on your old and new line, and use a coupler to join the 2. Not the ideal way to go about coax, but I think if you have no other options, it will get the picture on the tv!

Does anybody know if there ae any tech issues like mismatched impedance or similiar when you splice RG-6 to RG-59?