Minecraft doesn't get past the Mojang logo on Windows XP

Whenever I play minecraft on my Windows XP Computer, it crashes with a error EXCEPTION_ILLEGAL_INSTRUCTION (0xc000001d) at pc=0x04876630, pid=1220, tid=844

What I expected to happen was...:
Game to load, like it does on Linux on my same PC (Xubuntu)

What actually happened was...:
Mojang logo came up, and then error
*[15:25:38 INFO]: Client> # EXCEPTION_ILLEGAL_INSTRUCTION (0xc000001d) at pc=0x04876630, pid=1220, tid=844
[15:25:38 INFO]: Client> #
[15:25:38 INFO]: Client> # JRE version: Java(TM) SE Runtime Environment (7.0_51-b13) (build 1.7.0_51-b13)
[15:25:38 INFO]: Client> # Java VM: Java HotSpot(TM) Client VM (24.51-b03 mixed mode, sharing windows-x86 )
[15:25:38 INFO]: Client> # Problematic frame:
[15:25:38 INFO]: Client> # C [twitchsdk.dll+0x16630]
[15:25:38 INFO]: Client> #
[15:25:38 INFO]: Client> # Failed to write core dump. Minidumps are not enabled by default on client versions of Windows
[15:25:38 INFO]: Client> #
[15:25:38 INFO]: Client> # An error report file with more information is saved as:
[15:25:38 INFO]: Client> # C:\Documents and Settings\Alexander\Application Data\.minecraft\hs_err_pid1220.log
[15:25:38 INFO]: Client> #
[15:25:38 INFO]: Client> # If you would like to submit a bug report, please visit:
[15:25:38 INFO]: Client> # http://bugreport.sun.com/bugreport/crash.jsp
[15:25:38 INFO]: Client> # The crash happened outside the Java Virtual Machine in native code.
[15:25:38 INFO]: Client> # See problematic frame for where to report the bug.*

Came up.

Steps to Reproduce:
1. Get a AMD Athlon 3000+ XP Cpu, a Nvidia GeForce 6200 GPU and 1.25gb ram
2. Put Windows XP on it
3. Try to run minecraft

I have also included the log for it.