Im pretty sure that the router is not the problem. DHCP works the same, DNS works the same, NAT works the same, these have all been RFCd and standardized. It is possible that your NIC drivers are to blame, but then again, we really don't know unless we see some logs.
If your router is to blame, then the router is most likely defective and would need to be replaced by the vendor, but this would not cause a BSOD unless it is sending unwanted packets which would probably be caused by a compromised router (someone has access to it and is trying to execute code on your system), or other hardware fault.