precisely every second boot fails

[Magosányi Árpád]

It does not matter whether the machine crashed last time, it was a clean reboot or shutdown, after the BIOS the display is black.
The boot process might continue, but I cannot see it. The machine (Lenovo T530) have full-disk LUKS protection, so I cannot figure out whether it would boot up and find a correct display. Some times I was trying to enter the LUKS password, but no sign of booting.
If after that I turn it off and turn it on again, the machine boots normally.
lspci says this about the display controller:
00:02.0 VGA compatible controller: Intel Corporation Ivy Bridge Graphics Controller (rev 09)

ProblemType: Bug
DistroRelease: Ubuntu 12.04
Package: grub2 1.99-21ubuntu3.1
ProcVersionSignature: Ubuntu 3.2.0-24.39-generic 3.2.16
Uname: Linux 3.2.0-24-generic x86_64
ApportVersion: 2.0.1-0ubuntu11
Architecture: amd64
Date: Wed Aug 1 20:31:53 2012
ProcEnviron:
 LANGUAGE=en
 TERM=xterm
 PATH=(custom, user)
 LANG=en_US.UTF-8
 SHELL=/bin/bash
SourcePackage: grub2
UpgradeStatus: Upgraded to precise on 2012-04-30 (93 days ago)

[Magosányi Árpád (mag-magwas)]

Further test have shown that grub indeed works, only the display is black. X was the first thing seen.
After upgrading to kernel 3.3.6 per https://bugs.launchpad.net/ubuntu/+source/xserver-xorg-video-intel/+bug/993187/comments/91 now I can see the display as soon as kernel takes it. Grub splash screen and menu still black.

[Magosányi Árpád (mag-magwas)]

$ cat /boot/grub/video.lst
vbe
vga
video_bochs
video_cirrus

[Marcus Tomlinson (marcustomlinson)]

This release of Ubuntu is no longer receiving maintenance updates. If this is still an issue on a maintained version of Ubuntu please let us know.

[Launchpad Janitor (janitor)]

[Expired for grub2 (Ubuntu) because there has been no activity for 60 days.]