The standard Auto-Import feature would remove the dead links and import the video files from the new location. You would lose your library tags so it is not what you want to use.
You can restore a library backup file (File > Library > Back Up/Restore Library) and fix the base paths with the Rename, Move, & Copy Files tool. The tool has an option for replacing a part of the directory path in the library with another string without touching the media files at all. For example, you can change D:\Video\ to E:\Video\Music Video\.
Another option is to export an mpl playlist file of all videos and import the mpl file on the other PC. (File > Export/Import Playlist). An mpl playlist contains all library field data of the included files (but not view schemes or other playlists). The playlist export tool has an option for relative paths. If an mpl playlist with relative paths is exported to a base folder it will work on the new PC if all files and folders that are under the basefolder are still correct. It must be imported from the same relative location. For example: export to D:\Video\ and import from E:\Video\Music Video\ .
I'd recommend to switch the Auto-Import feature off before doing this kind of operations. Maybe you could create a small test library and test the workflow before doing the real thing.