Alright, guys… I fixed it.
Don’t know why, but I decided to DELETE the wp-admin folder ONLY from my server, leaving everything else. Then I DOWNLOADED and UNZIPPED the entire WP package from www.remarpro.com. Then I UPLOADED ONLY the wp-admin folder from this fresh WP package back onto my server.
Now everything works.
Seems kinda like voodoo-tech, but after replacing the entire package three times with no sucess, replacing only the wp-admin folder worked the first try.
Best of luck.