Did you have codes before the starting issue?
I would be heavily suspicious that the codes and non-starting are related. I wouldn't to quickly from there.
Vacuum leak - very very very common. Start at the air filter and work your way to the throttle body looking for any loose hoses or clamps. Twist each connection/make sure each fastener (bolt, clamp) is tight. Make sure hoses aren't cracked - partiuclarly the smaller ones underneath, etc. Make sure all are fully seated and tight. Additionally you can spray starter fluid around the intake hose (or probably brake cleaner/carb cleaner...if that's safe) while trying to start the car. Or put some gas into the intake then start. If it starts then you can guess you have leak.
Are you sure it has a brand new timing belt or do you mean the drive belt?
Timing belt would impact starting, not the drive belt.
If the timing belt *is* new - why is it new? Did it break, were you chasing other issues, this might help us diagnose?
What recent work has been done to the vehicle?