Both BSOD's are STOP 0xD1 in your networking drivers
Considering the presence of malware, I'd suggest posting over in the security forums to get a clean bill of health: System Security - Vista Forums
Once that's done, I'd then suggest updating your networking drivers
If you're still having problems after that, then I'd suggest:
1 - downloading a free antivirus application (I like Avira Free for 32 bit systems).
2 - uninstalling the Bit Defender Internet Security
3 - IMMEDIATELY installing the free antivirus and IMMEDIATELY updating it.
4 - testing to see if that fixes the issues.
Should you decide to reinstall the Bit Defender, be sure to download the latest version from their website - and then be sure to remove the free antivirus before installing Bit Defender.
2 - uninstalling Bit Defender Internet Security