Video records at high speed

If you mean just the one and the rest then it was probably recorded in Extended Play mode and nothing can be done.
Otherwise please explain your issues in more detail.

Videos recorded on one camcorder very seldom play back in another, due to the internal codes put on the tape by the original machine.

Unfortunately, no. By recording in fast mode, the camera captured fewer frames than usual. When played back at the normal speed, the action appears faster than normal. Because the camera recorded fewer frames, there is no way to make up for the images that were not captured. You could slow down the playback, but the result would be a jerky, jumpy video.
Now, if you had accidentally captured the video in slow motion, you could then throw away some of the intervening frames and recreate a normal-speed video.

Hello,

It is possible the tape loaded on the wrong side of the drive. If you romove the tape, look for slack and tighten up, try it again or another tape. Otherwise it is likely that a spring for the pressure roller is off or broken. This is not easially repairable.

I believe the setting you changed set the RECORD method, not playback. The video is recorded that way. There are some Video software out there that can rerecord a video at a slower pace, but do you want to spend the money? Try Ulead.com for a low cost program.

This is a really simple problem and easy to solve.  Unfortunately the videos you've recorded cannot be changed back because they have been recorded in Time Lapse mode.  
With the camera switched on in Video Mode turn the control dial on the back (this is the dial to the right of the LCD screen).  This will change the settings from TIME LAPSE to STANDARD.  There are actually 6 different modes but the best one for normal videos is STANDARD.  There is a HIGH RESOLUTION setting,  however these record fewer frames per second (fps) so whilst the quality is better per frame,  there are half the amount of fps so the the movie will look at bit jerky.
It's really easy to accidentally twist the dial when holding the camera,  so always check the icon in the top right of the LCD before recording to make sure its just a yellow camera in a yellow square.  
This should be problem solved for all future recording.

Though I don't know the details of your camera and the tape you are playing, one explanation could be that the tape was recorded in "extended play" EP rather than "standard play" SP. Some VCRs and some cameras are incapable of playing back in EP, a mode where the tape moves at half speed so you can record more on the same tape. The result is that the tape playing back at regular speed appears twice as fast and fast forward will be even faster.

Unfortunately, unless your machine can be manually set to play back in EP (usually it is automatic) the solution is to play it back in a machine that can handle EP.

Make sure you are shooting your movies in "Standard" mode. If you have the mode set to something else, especially "Time Lapse", the playback may not match 'natural' motion.

In any case, you can control the speed of the playback. When you first enter the movie playback mode, there should be a movie control bar along the bottom of the LCD. Instead of the "Play" button, select the "Slow Motion Playback" button (single arrow with single bar next to the normal Play button), and control the speed with the left or right arrows on the multi-controller.

Record in slow mo mode, then playback in fast forward mode ;) Problem solved. You'll see the video in normal speed.

Your camera has a capstan servo problem which is more than likely being caused by the capstan motor itself.Nothing you can do youself,would suggest bring to service but reccomend getting estimate before repairing.