I've got one of the following vga to HDMI converters (as I've got a very old laptop)

http://www.amazon.co.uk/ESYNiC-1080P...hdmi+converter

This used to work fine on my old Samsung to but I've now bought a new Samsung UE50JU6800, and this won't recognise the HDMI cable when I plug it in.

Does anyone have any ideas why?

Either your old Samsung accepted PC resolution signals (eg 1024x768, 1280x1024, 1280×900 etc ) via HDMI but the new set only accepts HDTV resolutions (1920x1080, 1280×720 etc), or you had the PC set up right before but the new TV has forced the PC output back to generic PC resolutions.

Try setting the PC output to 1920x1080 pixels.