Hello Brink, many thanks for reply.
I've tried the Default File Type Associations - Restore
for .mp4 and .lnk but this didn't fix the problem.
However you showed me the right way (that means the registery database) and now this problem is fixed.
In HKEY_CLASSES_ROOT, and with a lot of patience, I've noted all keys and values associated to video file types which were not affected by this problem (I performed it with . avi and .wmv types). I've noticed that registery inputs are the same for this 2 kinds of files (see attached Reg_AVI and Reg_WMV documents).
Doing the same with .mp4 extension it was easy to highlight some differences (see attached Reg_MP4 document).
These differences make me think my problem was due to a bad Quicktime installing or unistalling, putting some trouble in the .mp4 key, that's why, I think, windows (via control panel) was enable to correctly manage shortcuts to .mp4 files (even if these files were correctly played in media player).
After having manually replaced keys and values on the basis of .avi type, problem was solved
I hope this post could be useful to someone.