Everything you say suggests you believe the catalog contains your images- it does not!
You cannot just copy a catalog to another computer and export new images.
The catalog must be linked to your original camera image files where they are stored, and if you 'move' a catalog it will lose all links to the original camera image files making export impossible.
May I suggest- Download and read the "FREE Lightroom eBook" at this site-
As stated above. The Catalog files does not hold all your images. It is just a database file that References your images store on your hard drive. What you need to do is copy over all your images from the Mac to the Windows PC and then Re-Link them to the copied catalog file by using the Locate missing folders and files system built into LR.
I know that it is just a catalog database, and I have linked them to the original raw files, and it still doesn´t work. I have done as I´m supposed to do and it doesn´t work.
What exactly do you mean by these statements.
"I have linked them to the original raw files"?
Linked them how? The LR catalog is looking for the images on the Macintosh HD (or just a /) SomeFolderName/AnotherFolderName(Maybe)/Pictures/.
Even if you copied all your images from the Mac to the PC the LR Catalog would need to know exactly where they are. That would now start with a Drive Letter, not a Name, like C, D, E or whatever.
"And it still doesn't work. I have done as I'm supposed to and it doesn't work".
What Doesn't work? What exactly have you done?
No one here knows what you have done and or why what you have done isn't working.