Unfortunately the problem you describe is one of the symptoms of the
notorious "lens cap" image sensor defect, and which would have qualified for a special JVC free repair as the model mentioned is on the list of models susceptible to developing the problem, "would have" being mentioned as the free repair offer was only valid up to the end of June 2009 after having been running for nearly three years, the qualification on receiving the repair
being that the person requesting it had to be the original purchaser of the device and have proof of this fact, the "original" purchase receipt being the usual item shown although credit card receipt proof can usually also be accepted.
Of course its not completely unknown for JVC to "sometimes" carry out a goodwill repair without this, but it all depends on who deals with the request, as this qualification was made to stop dealers buying up defective camcorders on the cheap, getting them repaired free, then selling then on at a profit.
I would contact JVC customer services on the UK phone number of 0870-330-5000 as you have nothing to lose as they might well oblige and carry out the repair, as experience has shown that this "has" still been done for quite a few since the passing of the official expiry date, and once again dependant on who answers the phone call so I would persevere on this.