Problems with New LEGO Cargo Train
I would start by breaking down the problem into a few simple checks:


Take the battery pack out of the engine of the train and press the green button. Does the green LED light turn on? If no, there is likely a problem with either the batteries or the battery housing itself. You might want to take all the batteries out and reinsert them, or rotate the batteries a bit when they are inserted (I have found that this sometimes improves the contact they make).
Put the battery pack back in the train, and connect the train motor directly to the battery pack (i.e. do NOT connect the IR receiver in between the motor and the battery pack). If you press the green button on the battery pack, do the wheels of the train spin? If yes, do they spin fast? If the battery pack refuses to turn the wheels, there might be a problem with the train motor (but there could also be a problem with the charge level of the batteries).
Assuming both the battery pack and the motor work fine, now connect the IR receiver between the battery pack and the motor. Look closely onto which of the two connectors you put the motor connector (red or blue).
Check the remote and make sure it has batteries inserted and that the batteries are inserted in the correct direction. Press one of the red buttons on the remote. This should make the green LED light in the middle of the remote light up. If it doesn't, you have either not inserted the batteries right, or they have come loose, or the remote control is broken.
Using the remote, turn the control knob of either the red or blue control section (depending on where in step 3 you connected the wires) and see if this makes the motor turn. If it does not, try turning the knob further. Also, make sure that the receiver is in direct line of sight from the remote control (you should be able to see the black curved top of the IR receiver from where you are standing with your remote control)
If the wheels still do not turn, check the channel setting of the remote and the IR receiver - they should be the same. Try again to turn the knob once you set them both to the same channel. If that still does not work, try different channel settings (e.g. both on Channel 2, both on Channel 3 etc) - you might have some interference from another IR source.
If after all this the wheels on the train still do not turn, you have a defective motor (it might have burned through because of too much resistance etc.). Try calling LEGO Customer Service (in the US, their number is 1 (800) 835-4386) or visit them online. If you have a LEGO store nearby, you could ask them to assist as well, though all they can do is do an exchange which they may or may not do depending on the state of the unpacked set.


Good luck and let us know what happens ...