The burner lit as indicated by blue flames. But only for a minute or two and then it went out again. At least I know that the igniter and the gas valve work. I have no idea on what to do next. Correct me if I'm wrong, but it looks like there's only one pressure switch for this model.

Check out the following link it worked on mine.
Just grab a small piece of fine sand paper. Make sure your system is turned off and cool. Next to the last burner you will find a sensor it will have one wire attached. Just feel along that sensor it will have a crook at the end now gently rub the sand paper around the end of it.
Hook it back up turn on your system... and enjoy.

http://www.justanswer.com/hvac/84c5a-trane-xe-80-burners-wont-stay-lit-cycle.html

Always start with the flame sensor. Remove and clean with light sandpaper or coarse steel wool.