I found the reason why FireWatir was not working at my machine.
Installation guide for FireWatir in step 2.e. says:
Close Firefox. Restart it again using command “[Firefox installation directory]/firefox.exe –jssh” from command prompt.
I opened Command Prompt at Firefox installation directory and copy/pasted "firefox.exe –jssh" (of course, without quotes) there. Pressed enter.
The next step (2.f.) is:
To check if JSSh is listening on port 9997 run command “telnet localhost 9997” from command prompt.
I copy/pasted "telnet localhost 9997" (also without quotes) to command prompt, pressed enter and got error message.
It took some time and a pretty long conversation at wtr-general mailing list to find the solution to my problem. At the end, I found it myself.
It seems that Word Replaces hypen (shorter -) with dash (longer –).
You can find that setting here:
Word (2003, service pack 2) > Tools > AutoCorrect Options... > AutoFormat > Replace > Hypens (--) with dash (–).
When I replaced dash (longer –) with hypen (shorter -) in "firefox.exe –jssh", everything worked just fine.
What have I learned? Never write documentation in Word. Do it in Notepad.
The whole conversation is here.