1999 Sable will not start after a few trips

I seem to have the same problem as some of the other Sable owners. Car starts fine the first time, I can drive it 20 miles to work, it'll sit there for 10 hours, and it will start again and get me the 20 miles back home. After I shut it off in my garage, I try to start it, but will only get about 300 rpm for 30 seconds, then it stalls. The next morning, it will start up again and get me to work! I replaced the fuel filter, and can hear the fuel pump motor start up when I have someone turn the key while I listen down the filler spout. Any ideas??

I am going to say to check the IAC (Idle Air Control) valve. This is a fairly common issue with the 3.0L V6 engine in these vehicles.