I was similarly ill on a plane once, however because it was before taxi, I had the sense and the opportunity to get off the plane.
Everything was fine at first. Getting to the airport, going through security, boarding..then a few minutes after I settled down in the seat I began to feel that something was seriously wrong. I got up in a panic, fought my way upstream to the F lav (I was in F), and proceeded to deflate from both ends..luckily I made the right choice (sit or stand? top or bottom?)...sat on the toilet, emptied, and projectile vomited onto the inside of the door of the lav. It was a horror show in there. Obviously the FA heard the commotion and began knocking on the door. When I opened it I saw the look of horror on her face, and I felt not only deathly ill, but terribly embarrassed as well as she had to deal with it, and the flight had not even taxiied yet.
I told her I couldn't fly, and they were good enough to let me off. Sadly, this was one of the rare times I checked baggage, so that had to be sorted also. I am sure I caused the delay as the flight ended up leaving 45 mins late. I also got sick again in the terminal.
Not sure what it was..after a 3rd round I was completely fine save for being exhausted, humiliated, and stuck in a distant city having to sort it out. But I did feel lucky that I got sick before it was too late and I had to endure the 5 hour flight like that.