There are a couple of issues in the logfile. First time you ran Wubi it found an \ubuntu directory already present.
The second time it downloaded the preinstalled disk image ubuntu-12.10-wubi-amd64.tar.xz, but the download was incomplete, so extraction failed:
11-22 01:11 DEBUG downloader: Download start filename=C:\ubuntu\disks\ubuntu-12.10-wubi-amd64.tar.xz, url=http://releases.ubuntu.com/12.10/ubuntu-12.10-wubi-amd64.tar.xz, basename=ubuntu-12.10-wubi-amd64.tar.xz,
length=562061340, text=None
11-22 02:02 DEBUG downloader: download finished (read 207376145 bytes)
11-22 02:02 DEBUG TaskList: ### Finished download
11-22 02:02 DEBUG TaskList: ## Finished get_diskimage
11-22 02:02 DEBUG TaskList: ## Running extract_diskimage...
11-22 02:02 ERROR TaskList: Extraction failed with code: 2
After that you had a CD in G:\, but this isn't a valid image as it is failing the md5sum check. I noticed that the md5sum shows two different invalid md5sums, so I assume you have tried two different CDs (or mounted two different ISOs):
12-14 12:07 DEBUG Distro: checking whether G:\ is a valid Ubuntu CD
12-14 12:07 DEBUG Distro: parsing info from str=Ubuntu 12.10 "Quantal Quetzal" - Release amd64 (20121017.5)
12-14 12:07 DEBUG Distro: parsed info={'name': 'Ubuntu', 'subversion': 'Release', 'version': '12.10', 'build': '20121017.5', 'codename': 'Quantal Quetzal', 'arch': 'amd64'}
12-14 12:07 INFO Distro: Found a valid CD for Ubuntu: G:\
12-14 12:07 INFO root: Running the CD menu...
...
12-14 11:48 DEBUG TaskList: #### Finished get_metalink
12-14 11:48 DEBUG TaskList: New task get_file_md5
12-14 11:48 DEBUG TaskList: #### Running get_file_md5...
12-14 11:49 DEBUG TaskList: #### Finished get_file_md5
12-14 11:49 ERROR CommonBackend: Invalid md5 for ISO C:\ubuntu\install\installation.iso (7ad57cadae955bd04019389d4b9c1dcb != 4d30a270cc24c85b33daa9d82d95b04d)
None
12-14 11:49 DEBUG TaskList: ### Finished check_iso
12-14 11:49 DEBUG TaskList: ## Finished use_cd
12-14 11:49 DEBUG TaskList: ## Running extract_kernel...
12-14 11:49 ERROR TaskList: Could not retrieve the required installation files
The correct md5sum for that ISO is:
7ad57cadae955bd04019389d4b9c1dcb *ubuntu-12.10-desktop-amd64.iso
So the solution is to download the ISO again and if Wubi fails, check the log file to see if the md5sum is good.
A couple of points for installing... if you want to install with Wubi (inside Windows) then you should place the downloaded ISO in the same directory as wubi.exe before running Wubi. If you burn it to a CD or mount it as a CD, then it will offer the "CD menu" which doesn't include the "Install inside Windows" option. (Or you can run it off the CD with the --force-wubi option).
Also, for computers purchased with preinstalled Windows 8, Wubi doesn't currently work due to lack of support for GPT disks - I think it's okay in your case as it says you have a 32 bit version of Windows 8).
Finally, you can install Ubuntu by booting from the CD AND keep Windows. The Ubuntu installer (ubiquity) will offer to split Windows and create a side-by-side dual boot install (except in certain cases where you have used the max partitions). This is the best solution if you want a permanent Ubuntu install (Wubi is more to try out Ubuntu).
Best Answer
This is the problem:
I know this is an existing bug in the development release 13.04, but I wasn't aware it was in 12.04.2 as well. There is no workaround to this, because you'd have to update the ISO (possible but painful).
Reference: https://bugs.launchpad.net/wubi/+bug/1134770 (just updated with this latest info).
Workarounds
You could either use the 12.04.1 Wubi.exe with the 12.04.1 ISO available at old-releases.ubuntu.com/releases/12.04.1/ Or you could use the 12.10 Wubi.exe plus the 12.10 ISO.