I know timeframe is now too short , but
take the PC into Noel Lemming and tell them : replace it . It was obviously assembled with faulty parts . The HP tech would know that .
Its up to NL to sort out Warranty, thats the NZ law (CGA). NL will have more powers of 'persuasion' with HP
If NL start trying to fob you off, mention CGA . You dont have to deal with HP, at all.
Take your ph & tell them you will be recording the conversation : by law they cant mislead you over CGA rights .