It feels like his death was my fault.?

My dad died suddenly on the 6th July 2006. He had a very sudden heart attack and ped away whilst alone in the house. Around a week or so beforehand, he'd contracted a bad cough and chest infection. I was on the computer at the time, he was sat behind me watching the television. I heard him mumble something so turned around to find him clutching his chest and his legs stuck out. I asked him what was wrong and he replied his chest just felt tight and he felt a little short of breath. It ped after about 30 seconds and we both returned to what we were doing. About a week later I was taken out of school and told that my Dad had died. After the initial shock I realised that what I'd experienced the week before may have been a forewarning heart attack. I've beaten myself up about it ever since his death. I feel a copious amount of regret for not probing him more or encouraging him to go to the hospital. I'm too afraid to tell anybody because his loss was so great. I don't feel as though I have grieved properly for him or as though I've cried half as much as I should have. I feel as though I have a huge weight hanging around my neck but most of all I feel guilt for taking away a father, a husband, a cousin, an uncle, a friend and a nephew from everybody.