since installing 10.04 my computer will not shut down

When the shutdown "five dots" screen appears, could you press key <ESC> and post displayed messages.
I don't fully understand the rest of message. Update-manager installed new version of kernel, and the last one don't boot. Can you confirm and provide in this case the kernel version. If it is the same version of future Maverick 10.10, I advise you strongly to wait before doing the upgrade.

at "five dots" screen, pressed key <esc>: this is the output:

Broadcast message from root@joe - laptop
      (unknown) at 5:58...

The system is going down for halt NOW!
Checking for running unattended-upgrades: init: Disconnected from system bus
modem-manager: caught signal 15, shutting down...
init: usplash main process (4457) terminated with status 2
   * Asking all remaining processes to terminate... [OK]

illall5: omit pid buffer size 16 exceeded! [OK]

* Deconfiguring network interfaces... [OK]

* Deactivating swap... [OK]

* Unmounting weak filesystems...
umount: none busy - remounted read-only [OK]

* Unmounting local filesystems...
[ 4103.947520] EXT4-fs: mballoc: 998 blocks 84 reqs (62 success)
[ 4103.947586] EXT4-fs: mballoc: 664 extents scanned, 2 goal hits, 24^N hits, 0 breaks, 0 lost
[ 4103.947662] EXT4-fs: mballoc: 33 generated and it took 794397
[ 4103.947712] EXT4-fs: mballoc: 811 preallocated, 299 discarded
                                                                                                                                                                                                [OK]

* will now halt
                       [4104.127062] md: stopping all md devices.
[4105.261516] sd 0:0:0:0: [sda] Synchronizing SCSI cache
[4105.262002] sd 0:0:0:0: [sda] Stopping disc
[4106.356894] ipw 2200 0000:02:04.01: PCI INT A disabled
[4106.357658] ACPI Preparing to enter system sleep state S5
[4107.416229] Clocksource tsc unstable (delta = -492221751 ns)

Also, here is my login screen where I can choose which OS to boot the computer into:

Ubuntu with Linux 2.6.31-25
Ubuntu with Linux 2.6.31-25 (recovery mode)
Ubuntu with Linux 2.6.31-24
Ubuntu with Linux 2.6.31-24 (recovery mode)
Ubuntu with Linux 2.6.31-23
Ubuntu with Linux 2.6.31-23 (recovery mode)
Ubuntu with Linux 2.6.31-21
Ubuntu with Linux 2.6.31-21 (recovery mode)
Ubuntu with Linux 2.6.31-21
Ubuntu with Linux 2.6.31-21 (recovery mode)
memory test (memtest86+)
memory test (memtest86+, serial console 115200)
Microsoft Windows XP Home Edition (on /dev/sda2)

The bottom or first install of Ubuntu with Linux 2.6.31-21 and the (recovery mode) from that install will boot up,
but will not shut down properly. None of the other installs will even boot up to begin with.
Windows XP boots just fine when I occasionally want to use it.

The fact that you are unable to boot from 2.6.31-22 to 2.6.31-25 is strange. If would mean than now Linux kernel are unable to manage your hardware. What happens exactly when boot fails.
In shutdown messages, I see "ACPI Preparing to enter system sleep state S5". The next message should be "Powered down". I'm not an expert in this field, but issue seems to be related to last step when processor power off computer.

1) Could you confirm you do a Power OFF and not a Hibernate/Suspend.

2) Can you turn off ACPI on Grub. For this see: http://ubuntuforums.org/showthread.php?t=1323023
Don't forget to do a
   sudo update-grub
before reboot, and then check again (and in this order)
a) shutdown of kernel 21
b) boot of kernel 22

When I tried to boot into Linux kernel 2.6.31-22 I saw on the screen: unsupported WMI interface
There was other stuff there, but this is what I caught before the screen changed with a broken band of green
across the center of the screen which was only there for less than a second and then a blank screen

1) Could you confirm you do a Power OFF and not a Hibernate/Suspend.
2) "When I tried to boot into Linux kernel 2.6.31-22 I saw on the screen: unsupported WMI interface" Is this related to the change I asked you to do ?

3) Do you have an Acer laptop (issue on acer-acpi) ?

yes, my laptop is an Acer
I have to actually power off the computer by holding down the power button until it turns off

acer-wmi manages power on ACER computers.
http://code.google.com/p/aceracpi/wiki/SupportedHardware

Could you give the exact model of your computer ?
Do you have a ATI radeon xpress 200 ?
What was the previous Ubuntu version ?

2) "When I tried to boot into Linux kernel 2.6.31-22 I saw on the screen: unsupported WMI interface" Is this related to the change I asked you to do ?

my laptop is an Acer 1681WLCi. From the list of supported/non-supported laptops at the Acer-ACPI link
you put in the last reply, I can see that the ACPI is not supported. I don't understand completely how
that works. I don't know about the ATI radeon xpress 200. I may run a program I have that evaluates
all the stuff that is on my computer and lists it for me to keep as reference. My thoughts for what to do
about this right now: just forget it until I upgrade to Ubuntu 10.10 in a few days, and see if the new release
solves the problem. If not, I will decide what to do at that time.
Thanks for all the suggestions and advice.
Joe Gunto

What's the status of this question ?
If it solved, could you mark it solved in Launchpad.
If a specific question solved the issue, could you mark it.
Else I will have some time tomorrow to look at it.