How do I create a simple program or script that will notify me when one of our servers is down?

We have about a dozen Windows servers in our office, some of which are virtual. Some of the less-essential servers go down on occasion and I don't know about it untl after a problem has arisen. For example, we have a fax server that will go down sometimes and I won't know until customers call and say they can't fax something to us.

I thought about running a batch file or script that would ping each server on the hour and let me know if the ping fails. Then I realized we have one server where being powered on isn't enough -- it must be logged in, so a startup program can launch (for some reason it won't start as a system service).

What can I do to monitor my servers in an old-school way that involves some simple scripting? I'd be willing to use an open-source program to handle it if one exists, but this isn't something I want to throw hundreds of dollars at (with a commercial program) when I know can do it for free either on my own or with a program someone else has already written for this purpse. I am decent with batch files and I've done some beginner stuff with C++ and VB scripting. What's the best way to attack this problem?