You are correct, typically in a three prong arrangment the two most outer prongs are HOT and the center is nuetral. At this point unless your comfortable using a voltmeter, the power source at the the receptacle needs checks, as the wiring may be defective. The voltage measurment from each HOT to NUETRAL should read 120V. You may have also connected the plug assembly improperly. Does the drum light go on? Is the breaker tripped? Have your landlord contact a qualified electrician and have the outlet checked out.

rpsinfoman has you on the right track.

I think it would be helpful if I add:

Inside the washer, the "neutral" terminal will have white or blue wires going to it. The hot leads will usually be a red and a black wire. However, some manufacturers will just use all red or all black for the "hot" and white for "neutral." (I personally have wired devices both ways depending on the circuit.)

The worse thing that can happen is you will trip a circuit breaker, so make sure the power is OFF before plugging in the washer. If you've made a mistake, the breaker will instantly "trip." If it does, just go back and try again.

This is from a self help website:

Here is a link that might be useful: Wiring a dryer cord

sometimes it's as simple as checking your breaker
check your breaker to see if it's on

Be careful, make sure you use a voltmeter. The worst that can happen is NOT a tripped breaker its a burned out dryer. Destroyed, dead, paper-weight. You should read 120v between neutral and either hot and 240 between the two hits. If you're mot sure, pay an electrician -it's cheaper than buying a new dryer. It is true that it's easy to change the cord-just be sure you know what you are doing.

This just happened to me. try bending the prongs that plug into the socket. cheap cable just didnt have a good conection. now it works perfect

The dryer had a ground for a reason. Many newer dryers will have a sensor to tell is there is a ground fault. If you disconnected the ground (The fourth prong was a ground) then the dryer may refuse to start due to a ground fault. It IS possible to be shocked by an ungrounded appliance. It is why a ground was added.