I would disconnect the cable and pop a continuity check across the conductor and shield and if possible, across the length of the cable to make sure you don't have a break in the braid. Another possiblilty is that you've been unlucky and cut the cable on a current node so may be acting rather too efficiently it's own antenna as you say, perhaps try chopping a few inches off one end and make a new termination. Having the cable coiled up won't help either
Also if you must use a splitter (no problem if the source signal is decent and you're not running miles of downlead), do yourself a favour and get a proper shielded one in a metal enclosure.