It could help if you can describe what happens in more detail.

From your post it appears that if the car has been sitting for 12 hours it is hard to start. It also appears to happen if the previous start was allowing the engine to run for only 15 sec. Do these both have to be true for the hard start? What if the car is started in between times and driven normally? Also when the car finally does start does it run smoothly right away? How does it run when warmed up?

The replies point to loss of fuel flow or low fuel pressure (maybe a bad fuel pump?). They also suggest a bad temp sensor. If the temp sensor is stuck "hot" (short circuit) or the pressure is low the car will run very lean and may die repeatedly after a cold start. If the temp sensor is stuck "cold" (open circuit) then Klaus's suggestion of flooring the pedal while starting may work because the engine is likely to be flooding quickly. If the fuel mixture is too rich the car will probably run worse and eventually quit as the engine warms up.

I think some of the computer control functions don't operate until the engine has been running for a few minutes. If the fuel mixture is not very far out of spec you may not get a warning light until you've driven on the highway for a while.