If the year tags are shown in other applications then the tags are probably in the files. If some programs don't show the tags, then the tag format may be a later version than that program can read. For example the program may only be able to read ID3v1 tags, while the tags in your files are in ID3v2.3 format.
If you want to see what tags are actually in your files, click on an audio file, then in the Action Window click on "Tag", then up the top you will see some information about the file, in the form something like "MP3 - 1:47 - 1.6MB", right under the Tag heading. When you hover over that information you will see it is a hyperlink, as it becomes underlined. Click on that link and all the tags that are actually in the file are displayed, as opposed to those in the Library.
Anyway, if the tags are in your files, but not in your library, select a file then right click on it, select "Library Tools", then "Update Library (from tags)". That should put the year tag into the MC library and make it visible to you. If you are happy with what MC did, select all the files you want to fix, and run the update for all of them. Perhaps do them in chunks so that each run doesn't take too long, and check you aren't getting a result you don't like. There may be other tags in the files which may overwrite the tags you already have in the Library.
Make sure you back up you Library before you start, so that you can revert if something goes wrong. File/Library/Back Up Library.
Done.