Why would a Mercury Mystique turn over but not start even after a jump?

I had the same problem on my 1996 Pontiac firebird, they told me that my ignition cylinder had went out. Maybe you could ask about that, I don't know what would cause that to go out though?

I had a similar problem 1998 Mystique LS. It was a burnt out relay. Also the ignition switch (what the key turns on...I'm not a mechanic I think that is what it was called) was worn and I had to replace switch.