We don't typically post logs here.
You can submit your logs with a bug report, if desired.
However, looking at the logs, one item jumped out at me.
0x8000FFFF
That error basically means that something caused a catastrophic failure of the installer, but the exact cause can't be determined.
The subject error, that you posted, 80004002 is also a rather generic failure, and is often associated with Windows Update.
See if this link -
http://www.binzywu.com/2009/07/live-mesh-win2008-80004002-error/ - which describes updating the WU Agent - solves it.
If not, then it is possible that your prior removal of Live Mesh was incomplete and that the errors are due to crashing into bits already on the PC.
See the information in this thread for how to manually remove the bits:
http://social.microsoft.com/Forums/en-US/LiveMesh/thread/e22e0115-98d1-47eb-b495-ff3e10acb0a6#a6bb9a90-9629-4571-9975-b8cc5cc26569Failing that, submit a bug report with your servicing logs:
How to Submit Bugs and Live Mesh Logs
Note that you may not receive a response to the bug report, though. It will be transferred to the internal system to be assigned to the appropriate development group.
-steve
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