if it is actually the lead that's faulty, or the connectors in the machine. You'll only find out by trying a new lead.
The machine should still be under warranty - you can check by looking at the warranty document that came with it, but in any case I should talk to HP - they're usually very helpful.
Call them on 0870 010 4320 between 8:30 a.m. and 6:00 p.m Monday to Friday, and 10:00 a.m. and 4:00p.m. on Saturday