Overview:
The concept of switchable Graphics support in Linux - whether ATI & Intel, or NVIDIA & Intel - is currently in development.
Various workarounds are available, but I suspect strongly, these issues will be eventually resolved, but you may have to wait some time for stable solutions.
In the interim, may I suggest you look at the latest graphics drivers and an updated Kernel.
In my experience, if the boot/shutdown issues are not Power Management related, then they are most often Graphics related.
Remember - use a good imaging tool such as Clonezilla so that you can easily rollback if stuff goes wrong.
Updating your intel drivers & mesa stack:
The latest "bleeding edge" intel drivers can be found by adding the Edgers PPA. These work best with the 2.6.39 kernel.
These drivers can be very unstable - but given your current graphics issues, it is worth a try.
sudo add-apt-repository ppa:xorg-edgers/ppa
sudo apt-get update
sudo apt-get upgrade
this should update your graphics including your intel driver. If it doesnt then
sudo apt-get install xserver-xorg-video-intel
Assuming this works - my recommendation would then to be to disable the xorg-edgers ppa from your software sources. Updates to this PPA are frequent - and there could be a strong possibility that one or more updates could break your system.
Before you upgrade from the PPA again - take a quick image backup just incase the revised updates breaks your system.
By fortunate coincidence, the latest ATI Catalyst driver (11.6) can also work with the same 2.6.39 kernel - see the AU question and answer.
If you couple both the intel and ATI updates with the vgaswitcharoo trick - together with the latest Kernel, hopefully this should resolve both the boot & shutdown issues as well as most of your graphics issues.
Before upgrading to 11.10
Before you upgrade to 11.10 when it is finished in October this year, you should "ppa_purge" the xorg-edgers PPA as well as remove the ATI Catalyst driver.
This should allow you to upgrade successfully.
