My advice is to hold the lock button and the home button. Release the lock button after 10 seconds and keep holding the home button. This places the phone in restore mode. Update your iTunes back to normal and install firmware 1.1.1. No need for only 1.0.2 any more, 1.1.1 has almost been perfected.
Once you have that fixed, all you have to do is go to
www.jailbreakme.com and click install, wait 30 seconds or so(depending on internet speed) and it will ask you to slide your iPhone to unlock it. When doing so installer.app will be there and your done with a phone in 1.1.1 and jailbroken. No applications on the computer needed.