Seems to be quite straightfowrward.
MC has the path as \\Dan-pc\p\Midnight Oil\Diesel and Dust\01 Beds Are Burning.mp3
The computer's path is:P:\Midnight Oil\Diesel and Dust\01 Beds Are Burning.mp3
They are not the same.
Assuming all your music is on the P drive, you can fix this.
DO THIS ON ONE OR TWO FILES TO START WITH, TO TEST THE PROCEDURE
Select some of the affected files that are in playlists.
Right click and go to Library> Tools> Copy, Move, and Rename.
From the top left, select the option beginning with "Update..."
Then check the Find and Replace option (only).
Find: \\Dan-pc\p
Replace with: P:
When you hit the OK button, all the files that are in P:\, but the playlists thinks are in \\Dan-pc\p\, will be recognised. Use similar logic, if not all the files are on the P drive, or other variables need to be changed.