Don't know where to trouble shoot next. Car won't start

[tanya]

I bought this car a month ago to use a "beater" while I live in HI. I know it was parked for a year because the guy got it up and running to sell.

It has been fine as a commuter for the past month and it even started to drive smoother then when i bought it. Yesterday I took it on the highway on a hilly section at 60mph which I had not done before. It started to shutter and the check engine light came started flashing. I pulled over, shut it off ans then restarted it. It drove a few more miles and then was running rough again and the check engine light was still on flashing and then went solid. I pulled over again. This time it would not start. There were no tow trucks availbale so I waited and then tried again. It started and I drove about 10 miles at 30mph with very little power or acceleration and the rpm would rev. I slowed down to let others pass and it stalled. It took an incredibly long time to turn over but it started and I drove another 8 miles then had to slow on a corner and it stalled. I had it towed back to town.

I thought it might be the fuel pump so I pulled the back seat but that is running fine. When you turn the key it cranks but does not turn over. It sort of wants to catch but will not. I ran the battery dead and then had a mechanic bring a new battery. That did not work. He pulled a cylinder one misfire code. He pulled the spark plugs and 1 and 2 were very charred with lots of carbon. He replaced all the spark plugs and tried to get it start with starting fluid . It sounds like it wants to turn over and then even more when he squirted the starting fluid but will not. He suggested maybe a head gasket but based on what i am reading I do not have the milky oil or smoking exhausted. I have smelt exhaust a few times since I have owned the car but I do not think there was any smoke.
Any suggested further testing?