They waited in vain because their house didn't show up on the North West Ambulance Service's (NWAS) computer system. Like other ambulance services, NWAS uses the Ordnance Survey to update its address records.
"We tried and tried but could not get the sweet out. Barry tried the Heimlich manoeuvre but it was no use. We were relying on that ambulance," says Lindsey, who has three other children.
"The woman on the phone kept saying 'it should be with you', but there was no sign. We could not even hear any sirens. It went on for about seven minutes and by that time Kane did not stand a chance - he had gone blue.
"I do not understand how this could happen. The road was built in 2007 and we are in the A to Z.
We get post, takeaways, everything - but not a ambulance to save my little boy's life.
Our house was only built in March but we have had no other problem.
"Kane loved being outside and tragically that is why we moved to this house, so he had a garden to play in.
"Everybody loved him, he was such an amazing boy. He was autistic and could not speak but had such personality. His funeral was packed - we could not fit everyone in the crematorium.
"My daughters are distraught. It was terrible for Olivia, who he was so close to. She is 13 and watched her brother die in front of her.
So many new estates are being built all the time - is the ambulance service saying this risk is there for all those houses across the country. It seems unbelievable. We understand mistakes do get made and technology goes wrong but they are basically saying the system does not work for newer addresses.
A spokesman for North West Ambulance Service said: "We offer our sincere condolences to the family for their tragic loss. We have investigated this incident fully and shared the findings with representatives of the family.
"We will meet with them to talk through any further concerns if requested."
Stephen Twigg, MP for West Derby, has taken up the family's cause and has arranged a meeting with health secretary Andrew Lansley to highlight the problem in the system.
"This is a tragic case and one that North West Ambulance Service needs to provide answers to. That is the very least the family deserve," he said.