This has been my BIGGEST problem with the newer kernels. There has been a bug with the Intel Arrandale chipsets, which are causing suspend/resume to break. The problems include blank screen on resume, computer not booting up, etc.  I have a Core I7 Latitude E6410 and I was simply being screwed because of the suspend issue.

There is a temporary workaround posted by Paulo Silva - you need to first install the 2.6.38-rc3 (or rc1/rc2 but NOT rc4) kernel on your machine from here.

sudo dpkg -i linux-headers-2.6.38-020638rc3_2.6.38-020638rc3.201102010912_all.deb

sudo dpkg -i

linux-headers-2.6.38-020638rc3-generic_2.6.38-020638rc3.201102010912_amd64.deb

sudo dpkg -i linux-image-2.6.38-020638rc3-generic_2.6.38-020638rc3.201102010912_amd64.deb

Reboot.

When you suspend and resume, your screen would be dim - this is because the LCD backlighting is still switched off (unresolved issue). To turn it back on, press Fn+Left-Arrow.

Whew…

NOTE: An additional clarification - after resume, if you try to use VLC, the machine crashes with GPU errors. This is easily solved by turning off GPU acceleration in VLC.