There shouldnt be any problem with leaving your laptop or any laptop on for any length of time. There are poeple in this forum that haven't turned off their laptop in years, and only restart if Windows forces it (installations, updates, etc). So Dukefrukem, I am going to aggree with ASFx and say that your processor was a faulty processor in the first place.
Second, If you just keep the thing cool, you should have nothing to worry about. Keeping your laptop on while it is in the case on a road trip across America is not a good idea. If you can get a laptop cooler and let that cool the laptop continuusly, you should be in good shape. If you dont want to do that or want to cool your lap even more, you can throw your laptop into Battery Mode which cuts your CPU speed down. This results in less heat produced. If you need to do something high performance, just throttle it up. This works excellent for overnight downloads.
Also, if something on your laptop dies from leaving it on too long, the company should be obligated to fix it unless they explicitly tell you that you can't leave your lap on for an extended period of time. If they dont, then it is implied that this scinario is calculated into their laptop design and if something fails because of that design, it should be considered a faulty design (something not your fault) and the broken part should be replaced free of charge.
Personally, I dont leave my laptop on because I have a desktop that does all that overnight downloading, video editing stuff. I also dont mind the 20 seconds it takes for me to start my lap.