No. Sorry but it will not work. However, you can jailbreak with redsn0w or any of the other jailbreaks. Only difference is, you will need a computer to assist with the JB process instead of JB from the iPhone itself like you can with jailbreak.com.
Not to burst your bubble, but no you can't jailbreak with JailbreakMe with the phone you have. The easiest way to jailbreak is with Greenpois0n for you. Don't use Redsn0w, it's tethered for 4.2.1.
Greenpois0n works well with iOS 4.2.1. I was just correcting the other poster that said redsn0w was only a tethered jailbreak for iOS 4.2.1 when in fact it is untethered as well. Here is a link to Greenpois0n if you would like to use it. Jailbreak iPhone iOS 4.2.1