@ OvenMaster: all due respect, but, that's crap.
Warrantees start on the date of purchase. It helps, though, if you can produce a sales receipt/invoice (better still, if you registered the printer with HP when (or shortly after) you bought it. Records help - a lot.)
That said, no registration and no invoice = warranty does start on date of manufacture.
Assuming that you either registered the printer, and/or have (or, can get) an original invoice (both would be best), call HP again. Get your issue escalated to a CSR supervisor. You do have a history of service calls (here, it does help if you've documented them: dates, ticket number(s), etc) that go back to before your 1year was up. Explain your situation to the supervisor. Be polite! You'd be surprised as how much politeness (and, supporting docs) will get you.
I'm just speakin' from personal experience, sir. I'll rephrase my original post:
I hate to say it, but whenever my product warranty ended and I needed any free service afterwards, I was always SOL.
Whenever I've bought something and it busted any time after the warranty, no amount of niceness or bargaining or documentation ever got me even one bit of satisfaction. Maybe I patronize the wrong vendors? Hell, I've even been refused warranty service DURING the warranty term!
In all seriousness, I do wish Pjarbit all the good luck in the world in getting his issue resolved... I hope it's better than mine has been over the years.