HELP Ignition Problem
 

Firstly just wanna say hi to everyone as im new on here. Right i have a intermitant problem when starting my audi a3 (51 plate) it starts runs for a couple of seconds then dies and the small light with the car key symbol flashes up on the dash, if you leave the car for a few hours this problem goes away. However sometimes this problem has kept my car out of action for up to a day. My dad who is a self umployed mechanic has changed the ignition barrell ( for a brand new one to suite the original key) but still no luck??? I even have a fault code (0351 IGNITION LOCK TERMINAL S , OPEN CIRCUIT/SHORT) I got this from having it plugged into a local garage (not audi) If anyone has any info on this problem i would be very gratefull.