This could be "by design". Does the machine start as far as being able to get into the BIOS settings and see the health monitor readings (temperatures and such)? It could just be that the fan turns off as things are cool enough to allow it to, conserving power, and it'll turn back on later if needed. If you can get to the BIOS you should be able to see the current temperature of key areas. If they are low, all is well. If they are 0 then there may be a problem with a sensor. If they are too high then the fan should be on.
As a fail-safe fans default to being on, and at full speed, on power-up and remain so until explicitly told (by the BIOS or the OS) to be off or running slower. You should hear a rack full of 1U servers if they all power on at the same time - all those little high-speed fans creates quite a din for the first 30 seconds or so.
My Atom based netbook almost never turns its fan on, unless I'm in a hot room and/or ask it to run the CPU at full tilt for a few minutes, except for the few seconds after powering on.
Obviously, for safeties sake, make sure this is supposed to happen with your setup before leaving it running without fan for more than several seconds.