Why can't I run Minecraft on Windows vista?

People told me to install java so I did so, it still doesn't work. Everytime I open Minecraft through Minecraft launcher it crashes a few seconds later. Do I have to get Windows 7 or 8? Because apparently Minecraft should be able to run on Vista. I look at the developement console after the crash and the messages can vary, but often it will say,

A fatal error has been detected by the java runtime environment:

EXCEPTION_ACCESS_VIOLATION (0xc0000005) at pc=0x4db2ee80, pid1976, tid=19648

it also says: "failed to write core dump. Minidumps are not enabled by default on clients version of windows". Assuming that they're important, how do I enable them?

It also says that the crash happened outside the java virtual machine in native code and that the game ended in a bad state (exit code 1)

I tried to narrow it down to the parts that seemed important as it was pretty long, if anyone could help in anyway I would appreciate it very much.

Added (1). As you can tell I'm kind of a pc noob. My laptop is a Toshiba satellite L300D that has not been modded or customised at all. I think you should be able to know what specs I have from that but I'm not sure. I will do what you said and then update when done

Added (2). Windows® Vista® Home Premium Edition
AMD Athlon™ 64 X2 Dual-Core Processor TK-57
Toshiba TruBrite® WXGA TFT High Brightness display
120 GB
1,024 MB
DDR2 RAM (667 MHz)
ATI Radeon® X1250
maximum life: currently no official Windows Vista® battery benchmark result available
weight: starting at 2.49 kg
W x D x H: 362 x 267 x 33.0 (front) / 37.7 (rear) mm

according to some website these are the specs

Post your systems specs.

Run Window Update and download all updates. Run your antivirus and antimalware programs and have them remove any infections.

Do a clean boot.
http://support.microsoft.com/.../kb/929135

Then uninstall all versions of Java from Programs and Features. Download the latest version from https://java.com/...//java.com and install it.