Hi, just to clear up the definition dead, there is no such thing as a dead switch, it was never alive in the first place. You state that the switch powers on and powers off in a minute, that would be defined as a malfunctioning or defective powersupply.
I wonder what number you dialed where you talked to someone for an hour without getting anywhere? Also where you tried to register your product, to my best knowledge there is no need to register accept if you are entitled to contractual support.
All HP support contactnumbers can be found on http://www8.hp.com/us/en/hp-information/summary/ww-contact-us.html choose your country and go to "Technical support after you buy, that yould be in the third column. Lookup the number for "Network products" and most likely option 3 is ProCurve support (all depending on the local country).
There is also a possibility to open a ticket through the web. Go to http://h17007.www1.hp.com/us/en/support/converter/index.aspx enter your product model, select the correct version and click on display, there is a link to opening a web-case electronically (login is required).