You may be happier installing cygwin on that box to have a Unix-like environment in which to run your scripts. With a simple ps -efW you'll see not only the cygwin processes, but also the Windows ones. You might also want to run your checker (and perhaps the original tail-and-mail script) from cygwin's cron utility.

Also, a common way to check whether something is still running (actually running and not stuck somewhere) is to have it do something external (like touch a certain file or write into a log - a generalization of what bibo mentioned above) every once in a while and checking periodically whether this action has been executed recently enough. That may be better than simply checking for the existence of a process.

Have fun!