My questions: Do I need a router for protection? Will it significantly
improve my protection? When does "The Law of Diminishing Returns" apply if
it would help just a little?

I have been reading about security. One site said a router makes my
computer "invisible" on the internet. And another said "In very basic
terms, a router will automatically reject unsolicited inbound communications
to your PC. It will not reject solicited, but malicious, communications.".

I am running PC Tools Firewall Plus Free as my firewall and Avast 5 for
malware protection. I have spent some time to learn how to work theses apps
and set to most secure. PC Tools Firewall Plus Free was rated #2 firewall
at matousec.com. I always use my computer in standard user account. If I
need to use admin account I unplug network cable if I do not need internet
for what I am doing. I looked up the specks of my cable modem and it is not
a router. I use a direct network wire from modem to my computer. (I do not
use anything "wireless" yet)

I tested my firewall at grc.com ShieldsUP! It passed every test except it
failed the ping test because it responded to a ping. I also tested at
grc.com LeakTest v1.2 and it failed in a strange way. When firewall alerted
me to LeakTest v1.2 with the usual pop up warning "Allow or Block", I
obviously blocked it as instructed by leaktest instructions, and immediately
LeakTest v1.2 claimed it connected to grc.com and stated I failed the test.
I suppose this is off subject because it is a matter to take up with PC
Tools and grc.com.

Background info: Desktop AMD 4400+ 64X2 4GB memory 320GB HD Acer
(AM3100-U3201A) purchased new February 2008 -- 32-bit MS Vista Home Premium
SP2 -- MS auto updates on. Comcast ISP 12mbps service W\ Motorola SURFboard
SB5101 Cable Modem direct to computer. No other switches or routers or
wireless or phone line or any other networking hardware hooked up to this
computer.

Thanks for the help
Bob