ILO 42 inch flat screen tv

The coax cable connection is 1/2 inch screw type connection that sticks out from the back of the set. It has threads on it and has a little hole in the middle of it.

sounds like a cable issue, what time of source are you using to connect your tv to cable box ect??? hdmi dvi vga or coax???? I would start by changing that cable.

You simply need an "F" connector to "Belling-Lee" converter. about $4.00. At any Radio Shack, Antenna shop. This screw onto the end of the existing antenna connection & makes it so you can plug it into the Socket at back of set.
I have included a link that has a picture.
http://cgi.ebay.com/1-Coax-TV-Adapter-Connector-PAL-Male-to-F-Female_W0QQitemZ110386773163QQcmdZViewItemQQptZLH_DefaultDomain_0?hash=item19b3907cab#ht_683wt_1139

More likely the backlight inverter board has gone out, or power supply for the inverter board went out, those are the two places to look. Check the power supply first for burnt parts, bad capacitors.
http://en.wikipedia.org/wiki/Capacitor_plague
Please post back what you find

Simplest way I can think of, if you will have to get an HDMI cable box from your local cable service provider and just hook it up threw HDMI. There's your cable and in HD when available HD programing is on. :)

Since your TV only has audio and video input jacks, you can connect those to audio and video output jacks on the VCR. Now connect the coax cable to the RF/ant input on the VCR and you'll have to change channels by using the VCR channel selector.
Let me know if you require further assistance.

sounds like tuner control board

If you have cablebox, use RCA cable(composit) or componentcable to hook up. you will see better picture than repairing connector back on.

Depends on the make and model, possibly be the entire main board or the tuner board

The TV should have two ANT coax jacks in the back, one for air and one for the cable line. The one on the right side should be the one you want. It could be that you've plugged it into the left one, which will not work for line cable.