My money is also on something worse than coils... (Although the symptoms match)
I was pretty close to getting an '06. It's distant past, but I remember 04 and even 05's having teething issues that I wanted to avoid. One of those was a no-start if you only run it a short period and shut it off, but that wasn't the sole offender.
$2000 sounds generous.
(Hope you paid less)