I finally managed to fix it!!!
God, I am so happy right now haha
To anyone who might have had this particular problem, here is what I did to fix it:
0: uninstall all current drivers using AMD's own tool found on their website
1: downloaded this driver:
AMD Catalyst
2: tried to install the normal way (didn't work of course)
3: went to start > searched for "device manager" (without the quotations)
4: once inside device manager, find your graphics card and double click it
5: click the driver tab
6: click update driver
7: select the option to search manually for drivers
8: select "let me pick from a list..."
9: make sure the "show compatible hardware" button is flagged
10: select your driver, in my case it was called "ATI Radeon HD 4600 Series"
11: click next and wait for the driver to install
12: hopefully it says something like "Windows has successfully installed the driver"
13: reboot
14: driver installed
You should now be able to select the proper resolution (in my case, 1920x1080). If you have the black border as I did, open up AMD Vision Control Center (Or Catalyst Control Center if you have a newer card/driver), and select "My Digital Flat Panels", and then select the Scaling Function (Digital Flat Panels). Slide the scaler to the right until there is no longer a black border. That's it, you're all done!
PS: the funny thing is, that I already tried this earlier without luck, but with this particular driver it actually worked

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PSS: Thanks again to everyone who helped me in this thread, appreciate it
