Some Intel chipsets in the Intel 4 Series, most notably the Intel 965 Express Chipset are known to have issues with OpenGL support, causing newer versions of Minecraft to not run. (A full list of affected devices can be found here.)
If you see a crash report that looks like this, it means your computer is affected:
# EXCEPTION_ACCESS_VIOLATION (0xc0000005) at pc=*, pid=*, tid=*
# JRE version: Java™ SE Runtime Environment (7.0_51-b13) (build 1.7.0_51-b13)
# Java VM: Java HotSpot™ Client VM (* mixed mode, sharing windows-* )
# Problematic frame:
# C [ig4dev32.dll+0x3e88]
# C [ig4dev64.dll+0x55ec]
This error currently only affects all versions past 1.7.4 - and will likely affect all future versions of Minecraft.
As such, you may work around this error by playing a version prior to 1.7.4, such as 1.7.2. To play 1.7.4 or later versions, you will need a new computer.
For desktop users, you can purchase and install a new GPU, but the fact that your computer has an Intel 965 Chipset means that your computer is likely to be very old, and a new computer may be more cost-efficient.