Yes, it seems the router cares considerably. After much experimentation, I discovered a solution to all my problems with Avast! Entering a proxy in Internet Explorer did not work at all, however, by going into my router to "Port Forwarding" and designating port 12080 for Avast!, everything works perfectly with no other changes needed to any other software. I am not saying this will work for everyone, but it sure works good on my machine. Now I feel like the money I spent on Avast! was well spent.
By the way, I found "Tiny Forewall 64" works great with this antivirus, but you will want to completely disable your Windows firewall to run it. To do that, do the following:
1. Press the "Start Button".
2. In "Start Menu" select "Run".
3. Type "gpedit.msc" in the "Open:" box.
4. Expand the “Computer Configuration” section.
5. Expand the “Administrative Templates” section.
6. Expand the “Network” section.
7. Expand the “Networks Connections” section.
8. Expand the “Windows Firewall” section.
9. Select “Standard Profile”.
10. Double click the “Windows Firewall: Protect all network connections”.
11. Select the disabled option.
12. Select the “OK” or “Apply” button.
Then your Windows firewall will not only be shut off, but will also be greyed out.
AMD Athlon 64 FX-55 2.6GHz Processor (Clawhammer) Socket 939 CPU
GIGABYTE GA-K8NXP-SLI Socket 939 NVIDIA nForce4 ATX AMD Motherboard
GIGABYTE GV-NX68T256DH Geforce 6800 GT 256MB GDDR3 PCI-Express x16
Video Card
Corsair TWINX2048-3200C2 2 GB Kit DDR400 XMS3200 Memory
Thermaltake W0049RUC Silent Pure Power 680W Power Supply
Microsoft Windows XP Professional x64 Edition