Stuck with black screen on every first boot (no signal)

[g.ptic]

Recently, the following behaviour appeared suddenly:

1) Switch on computer
3) Instead of showing password entry for encrypted boot SSD, screen turns black and switches off (no signal)
4) Nothing happens
5) Forcibly restart computer
6) Everything works fine

This happens exactly like this every time I switch on the computer. Previously I had removed all but the latest 3.16/3.13 kernels, but this may be a coincidence because the latest kernels started without problems before.

UPDATE:
- Recently, the black screen always shows when booting the 3.6 kernel
- When booting from kernel 3.13, this problem does not appear anymore

(Set default kernel to 3.13 as a workaround)

Note 1: My OS starts from an SSD, encrypted via LUKS

Note 2: My graphics card is recognised as Mobility Radeon HD 5430

Note 3: Ubuntu HWE is enabled (Kernel 3.16)

Note 4: A similar problem also appeared at the same time on an Ubuntu 12.04 LTS 64 bit installed on a different SSD on the same computer: https://bugs.launchpad.net/ubuntu/+source/lightdm/+bug/1441305
However, there I got stuck with a black screen on *every* boot. In the end, changing the display manager to "gdm" fixed the problem.

ProblemType: Bug
DistroRelease: Ubuntu 14.04
Package: lightdm 1.10.5-0ubuntu1
ProcVersionSignature: Ubuntu 3.16.0-33.44~14.04.1-generic 3.16.7-ckt7
Uname: Linux 3.16.0-33-generic x86_64
ApportVersion: 2.14.1-0ubuntu3.8
Architecture: amd64
CurrentDesktop: Unity
Date: Sun Apr 12 19:41:35 2015
EcryptfsInUse: Yes
InstallationDate: Installed on 2014-07-23 (263 days ago)
InstallationMedia: Ubuntu 14.04 LTS "Trusty Tahr" - Release amd64 (20140417)
SourcePackage: lightdm
UpgradeStatus: No upgrade log present (probably fresh install)