Welcom to CD Freaks
To me, it looks like your setup should work, however there seems to be a loose video cable somewhere, particularly if you are getting audio, but no video.
If you get your Lite-On picture, ensure that you choose the source where the VCR is connected to (press the ‘Source’ button to switch between them). If no picture shows, but you hear audio, try unplugging the AV cables and swap two colours, such as the white with the yellow on both ends. If you get a picture now, then the yellow RCA cable is faulty. Otherwise, plug the cables back in with the proper colours and try a different AV input, such as the front AV inputs instead of the rear and switch the source to ‘Front AV’. If a picture appears this time, then there is a faulty video port on the original Lite-On ports you’ve tried. Otherwise, if you still do not get a picture, finally try connecting the VCR directly to the RF Modulator just to check if the Video RCA output on the VCR is working at all.
If you do manage to get this issue sorted out (such as finding a faulty/loose cable), then I would recommend connecting up your equipment using the following method, assuming that you will be removing your VCR once the transfer of tapes has complete:
[li]Connect the TV/AV-Out of your DVD Recorder to the RF-Modulator
[/li][li]Connect the Cable decoder to the rear AV-In on your DVD recorder
[/li][li]Connect the VCR TV/AV-Out to the front AV-In on your DVD Recorder
[/li][li]Connect the RF cables in the sequence - Aerial->Cable Decoder->DVD Recorder->RF Modulator->TV If you still use your VCR instead of the DVD recorder for recording TV, substitute the DVD recorder for the VCR in this sequence.
Hopefully one of these attempts will work.