Hi Chi-el,
Sorry for the slow reply. I think the problem is almost certainly that the processor needs the bootloader installed first. When the board was under production we did this at the factory, but if you are assembling one from scratch then you have to do it yourself. If you buy an Arduino Mega the bootloader already comes installed, but when using a new chip it is blank.
The bootloader only has to be installed once on each board, after that you will not need to do it again. I've attached instructions for how to do this, you will need to buy a USBASP device. They are very cheap, here is one from China but you can probably find European sellers on eBay who have them. Notice the one I linked to gives you the option of buying an 8-pin to 6-pin adapter, you will need this version because we use a 6-pin ISP port on the TCB. Most places sell them with the adapter included.
In the instructions I discuss a pogo adapter, you won't need this because your boards already have pins installed on the ISP port, so you can just plug in the 6-pin cable from the USBASP directly into your board.
The instructions also mention using an FTDI adapter to load the firmware. You can ignore this and just your USB cable to load the firmware as normal. The FTDI adapter is faster when we are flashing hundreds of boards, but you only have to do two of them so it's no problem.
I hope this helps, let me know if you have any questions!
EDIT: No, it doesn't make a difference what position the fight/repair switch is in.
Gosh, I sure wish this was posted in the TCB portion of Downloads! I have been scratching my head as to why my finished TCB boards (3 off) would not talk on USB, even going to the lengths of changing out one of the FT232 ic's in case it was a fake. Everything working fine now but sheesh that was a voyage of discovery I could have done without!