@rerrl Please check if BFBC2 is in the exception list of your antivirus/firewall software. You can try to check the game while your protection software is disabled. Run BFBC2 and Origin.exe as administrator and check if you are having any third party applications running which may interfere with your game. From your system specs, BFBC2 should run smooth on your system.
Check the online ports of your modem:
TCP: 18390, 18390, 18395, 18395, 13505, 13505
UDP: 18395, 18395
For specific instructions on how to open your ports, please visit http://www.portforward.com/ or contact your router manufacturer.
Cheers
Basti
