Yes, double check that the film is loaded correctly but, before trying to shoot another roll of film, try verify that the camera is working correctly by conducting a dry-fire test.
First, download and read over the manual if you don't already have one:
http://www.butkus.org/chinon/pentax/pentax_me/pentax_me.htm
Second, double check the battery. Install a fresh battery if you have any doubts.
While you have the battery compartment open, check for corrosion on the battery contacts. It is also possible that the battery contacts are bent or deformed. Check, clean and repair anything that is out of order.
Next, turn the camera on and operate it without film. Verify every function and check that the controls operate correctly and that they are set properly.
Operate it with the film back open and verify that the mechanics all work. Look through the film aperture and see that the shutter opens and closes as it should. Hold the camera up to a bright window or a light. You should see a flash of light through the aperture when the shutter clicks. Do this on all shutter speeds. It might not be possible to verify that the shutter is 100% accurate at all speeds but common sense should tell you that it's working close to spec. Check the bulb setting. When the release is held down, the shutter will stay open as long as the button is down.
Your camera has a self timer. While you are at it, check to see that the timer works correctly.
If the camera's electronics are working right, there will be a series of red, green or yellow lights in the left side of the viewfinder. They will light up to advise the photographer what the shutter speed or other settings are selected on the camera. If you have no lights or if they don't behave as expected, go back to square one. You might need to have the camera repaired if you can't figure it out.
Two things to note:
If the camera's batteries are dead, missing or if the battery circuit is non-functional, the camera should default to a given shutter speed. (Usually 125.) All the mechanical parts of the camera might still work but the meter and electronics will be dead. It will still be possible to shoot pictures but you will have to meter manually or guess at the exposure (aperture) setting. You will likely still get pictures but they may or may not be properly exposed. This is one reason why people are saying that your film might not be loaded correctly.
Second, the manual says that, after winding on to the next frame, DO NOT press the advance lever back until it is flush with the camera body. Doing so will shut the meter off. Many people have the habit of pushing the lever all the way flush but, on this camera, you shouldn't do that until you want to stop shooting and put the camera down.
Finally, after all the dry-fire tests have been done, you can put a roll of film into the camera. Better yet, retest with a roll of film that you can sacrifice. Either an old, expired roll of film or one you don't care about. This time, as you test, check to be sure the film is loaded and that the film motion indicator works.
On the back of the camera, there is a small rectangular window with black and orange (or black and white) stripes. These stripes will jiggle back and forth as the film moves through the camera. As you load and shoot, be sure the "jiggler" actually jiggles. It will also jiggle when the film is being rewound. Secondarily, the film rewind knob will turn as film is advanced through the camera. The jiggler and the rotation of the knob will tell you that the film is moving and that the camera is advancing correctly to the next frame.
After all this is done, load up a roll of fresh film and shoot some pictures. Evaluate them after they are developed. If the pictures come out, you're good. If not, the camera probably needs repaired.
