I downloaded a video in MP4 format, but when I tried to open it in quicktime player, it has no audio.
Unfortunately, the information given is incomplete and/or ambiguous at this point. I generally recommend posting either images containing a breakdown of data compression information detailing how the file was created or the uploading of a sample file for examination. I assume that your use of "MP4" here refers to the download of an "MP4" file container but does not confirm that the file does, in fact, contain some form of MPEG-4 (AAC) audio. While QTX/QT7 based media players expect MPEG-4 audio, such file containers can be created by third-party encoders using other audio compression formats. (E.g., for all I know at this point, the source file may contain DTS surround sound for TV playback which would be "natively" incompatible with most QT-based media apps.)
I don't even have a chance to export "audio only". Then I tried loading the video in iMovie, but I get the same result: no audio. I then tried opening the video using VLC, and it worked perfectly.
Excellent! When no audio is played by a QT media player, the first step is to confirm that the file does indeed contain an audio track. Your test confirms the file contains an audio track and implies that the audio was either compressed using a QT7/QTX incompatible audio format or employs non-standard settings that are incompatible with QT media player playback.
Can someone tell me how to fix this problem or tell me what's wrong with this video?
Unfortunately, without more specific information regarding the exact nature of the original problem, the only solution that can be provided at this point is a general one—i.e., recompress the file in such a way that it becomes playback compatible with your QT7/QTX based media apps. Optimally, you need a workflow that passes through video data without changing it but that re-compresses the audio data to a compression format employing settings compatible with your specific player, file container, and/or file distribution requirements. Since your requirements can be varied, so are your potential workflow options. Without more information (and since you have already indicated your system has VLC installed)—I would recommend you try using VLC to remux your original video to a new MOV or MP4 file container while simultaneously transcoding the audio as may be needed.
PS other videos have no problem using quicktime player
This merely indicates the files were somehow encoded differently.
