Non-chip can I travel to US?

Right, I have already asked whether my passport is valid but STA Travel and friends have made me paranoid! Passport issued in 2004, it's machine readable but I've heard you need a chipped passport...? I'm going to the USA soon and there's no one who can say 'yes you're ok'. Airline and travel agency won't give me an answer and refer me to the US embassy who I can't phone as my mobile network provider have blocked the ultra premium number and I don't have a landline and I can't call from work. I've got the ESTA but the conflicting info I'm getting on the passport is making me scared there's a problem.... can anyone help?