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I was watching a twitch streamer and people were asking about the modpack he was playing which also requires 64 bit java and he said that the license code on your laptop/desktop should work for 64 bit as well as 32bit.
I believe that from windows vista onward the installation cd's contained...
Your choice would be:-
Step 1 - Desktop graphics
Step 2 - Radeon HD series
Step 3 - Radeon HD 4xxx series
Step 4 - Choose windows version
Step 5 - Click display results
You never check for any driver updates using that method because afaik it only checks ms database of drivers which will be old. Go to the amd driver from the link below and get those drivers.
http://support.amd.com/en-us/download
Your username and or password is wrong. You should be using your email address as the username.
Edit: You are running windows xp and as such the only 1.6 pack you will be able to play is FTB Lite 2 that was created for 32 bit systems.
If the world is still in the saves folder then try the method below to get the world working again.
http://forum.feed-the-beast.com/threads/direwolf20-1-6-4-1-0-14-world-dissapeared.40499/#post-551684
I still say try and contact mojang and explain the situation and get them to verify the account holder is correct then supply them with a new password.
I would then suggest following the guide linked below. Please follow it exactly.
https://docs.google.com/document/d/17__CctJokfTCXovBs5YIdRhG39tdZlLMI_Mfq_aMu3k/edit
Remove all extra java versions you have installed then reboot. Now install the x64 one from here.
http://www.oracle.com/technetwork/java/javase/downloads/jre7-downloads-1880261.html
We would need to see a log when the crash occurs. If you care if you lose the world then take regular backups of it.
Edit: When the pack updates the mod pack makers always say to backup your world before updating.
If you followed the guide that was linked by lavarthan above then it should be installed on your desktop in a folder called FTB or on the c drive in the same folder.