Looks like your NIC driver caused both the BSoDs, update it:
Atheros AR8121/AR8113/AR8114 PCI-E Ethernet Controller(NDIS6.20)
fffff880`05674000 fffff880`05686000
L1E62x64 Thu Jun 11 08:45:22 2009 (4A30A802)
Also update this driver:
Asus ATK0110 ACPI Utility
fffff880`05686000 fffff880`0568e000
ASACPI Mon Mar 28 04:30:36 2005 (42476C4C)
I recommend that you replace Avast with MSE ,use the
Link Removed to completely uninstall Avast and then download and install
Microsoft Security Essentials.