Now the board is done, but I have one last problem, and that is that I don't know how to upload any code to the atmega8 on the board. I've followed other threads, but none of them helped me. I tried changing the board settings to ''Arduino NG or older'' and set the processor to ''Atmega8'', but it fails to compile the sketch (most likely because the code is not really meant for arduino). Is there a way I can upload code to the atmega8? And even more, to make the code be compiled in the arduino IDE?
The codes I'm trying to upload is in the documents section of the previous link (the RGB Serial Matrix Firmware).
I don't know how to upload any code to the atmega8 on the board
As far as I can tell, that board is not meant to have code uploaded to it. It doesn't have a serial port, and even the ISP port is unpopulated. There's no reason to expect there to be a bootloader. The sample Arduino code at the site is for a separate Arduino talking the the "permanent" Atmega8 firmware on the matrix board.
If you want to re-program the board itself: install the 6pin ISP header. Get a device programmer (perhaps an Arduino running the Arduino as ISP sketch.) Use the "upload using programmer" feature with the NG/Atmega8 board option.
I'll also decline to analyze unspecified errors. There's no inherent reason that the Arduino IDE shouldn't be able to compile nearly-bare C code; errors are as likely to be age-related...