Changing the region coding is only part of the problem. Region 2 DVDs are in the PAL video format and the U.S. uses NTSC. You need a DVD player that will convert PAL to NTSC, which yours won't. Outboard converters are expensive.
You'll have to buy a different DVD player if you want to watch Region 2 DVDs.
Regions 2's from Japan are NTSC. I'm not sure if it's all of Region 2, but I know for certain that Region 2 DVD's in Japan are NTSC. Just got a multi-region player and was playing a Region 2 NTSC DVD last night.
However, it might be simpler to buy a new player, such as a Malata that does PAL output/multiregion etc. Search for 'Malata' or 'skyworth' here or at AVS and you should find tons of info.
I have a Pioneer DV-440 and looking through the manual (pg. 52) it gives instructions on changing the Country Code. Would this allow me to view discs from other regions? The country codes appear to be 4 digit numbers, so I doubt it's the same thing.... anyone know for sure?