If you are comfortable doing some small repair work, you might be able to fix this with stuff you have laying around.
All you need is:
1 - 8" piece of coaxial cable with male connector on one end
1 - set of RCA cables (Red/White/Yellow)
1 - coaxial coupler
2 - small wire nuts
Take the back housing off of your TV. You may have to unscrew the small nut holding the threaded connector to the TV. This threaded connector should connect to the motherboard with a male RCA prong that should be soldered to the component on the motherboard. You will need to carefully cut
& remove the old soldering & wiggle the connector off. This is the hardest part, but it WILL come off with a little trying.
Now get your coax cable and strip off about 2" of the black outside housing ONLY. Your solid copper` interior cable should be protected by a small plastic coating which is covered in braided wire. You'll need to be careful not to cut the braiding off. Untangle the braiding down to where your cut stops and try and get it all on one side of the cable so you can twist it all together and make a nice wire. Now strip about an inch off of your interior plastic sheathing to reveal the small solid copper wire on the very inside.
Get your RCA cable and cut about 6" off of the one yellow side. Follow the same process above to get a braided sheathing wire and a solid copper wire. Attach this yellow wire to the coaxial cable by twisting the two braided wires together and the two solid copper wires together. Use your wire nuts & electrical tape to secure your connections making sure none of the wires can touch each other.
Connect the yellow cable's male prong into the component on the motherboard and attach your coaxial coupler to the male end of your coaxial cable. If you saved the small nut from earlier, you can re-attach this new coupler to the housing on your TV. Screw your housing back on the TV and you should be good to go.